It doesn't look like Voldemort ever saw Slughorn's memory as a concern.
As Bellatrix says, Voldemort could probably expect Slughorn not to tell anyone about the memory since he had sworn Voldemort to secrecy himself.
"But all the same, Tom...keep it quiet, what I’ve told - that’s to say, what we’ve discussed. People wouldn’t like to think we’ve been chatting about Horcruxes. It’s a banned subject at Hogwarts, you know..."
(Half-Blood Prince, Chapter 23, Horcruxes).
I think that Voldemort would've assumed that Slughorn would be too ashamed or intimidated to willingly choose to share his memory with anyone. He was apparently correct in this assumption; Harry only acquired the memory after severe coercion (plying Slughorn with liquor etc.). Voldemort's arrogance also lead him to the conclusion that, should anyone come to know that Slughorn knew him during his schooldays, Slughorn would protect him - either out of loyalty or fear.
Moreover, the actions of both Voldemort and Dumbledore indicate that Slughorn was never a viable target because of the memory.
Voldemort never tries to attack Slughorn. Even when he hires a Hogwarts student to try and carry out an assassination, targeting Slughorn never enters into the equation. Dumbledore is the sole target. It's true that Slughorn was given poisoned mead by Malfoy. However, Malfoy was clearly targeting Dumbledore and only saw Slughorn as a middleman.
“I’ve got butterbeer, I’ve got wine, I’ve got one last bottle of this oak-matured mead...hmm...meant to give that to Dumbledore for Christmas...ah, well...” He shrugged. “He can’t miss what he’s never had! Why don’t we open it now and celebrate Mr. Weasley’s birthday?"
(Half-Blood Prince, Chapter 18, Birthday Surprises)
"No harm has been done, you have hurt nobody, though you are very lucky that your unintentional victims survived...I can help you, Draco.”
(Half-Blood Prince, Chapter 27, The Lightning-Struck Tower).
If Voldemort had viewed Slughorn as a threat of any kind then he would've killed him - either in person or by sending an assassin. After all, Slughorn is presumably a much easier target than Dumbledore, who he was aiming to kill throughout Half-Blood Prince. Yet Voldemort seemingly has no concern in attacking Slughorn.
Indeed, when Dumbledore talks about the idea of Death Eaters visiting Slughorn he envisages them recruiting him, not attacking him.
“So, all these precautions against intruders, Horace...are they for the Death Eaters’ benefit, or mine?” asked Dumbledore.
“What would the Death Eaters want with a poor broken-down old buffer like me?” demanded Slughorn.
“I imagine that they would want you to turn your considerable talents to coercion, torture, and murder,” said Dumbledore. “Are you really telling me that they haven’t come recruiting yet?”
(Half-Blood Prince, Chapter 4, Horace Slughorn).
Slughorn's panicked reaction when he hears Harry and Dumbledore approaching his house may indicate that he is afraid of Voldemort, possibly because of the memory. He does go on the run when he hears that Voldemort is back. Yet there's no indication that Voldemort made any approach to Slughorn after his return and the fact that Dumbledore believed that Slughorn would sooner be turned than killed indicates that he himself believed that Voldemort wasn't likely to kill Slughorn over the memory.
This, I think, is the strongest proof that Voldemort never wanted to kill Slughorn (apart from the fact that he never attempted it). Dumbledore apparently never took any precautions to protect Slughorn. Dumbledore was well aware of the importance of the memory and yet made no attempt to protect Slughorn during the events of Order of the Phoenix.
Slughorn eyed Dumbledore balefully for a moment, then muttered, “I haven’t given them the chance. I’ve been on the move for a year. Never stay in one place more than a week. Move from Muggle house to Muggle house — the owners of this place are on holiday in the Canary Islands — it’s been very pleasant, I’ll be sorry to leave. It’s quite easy once you know how, one simple Freezing Charm on these absurd burglar alarms they use instead of Sneakoscopes and make sure the neighbours don’t spot you bringing in the piano.”
(Half-Blood Prince, Chapter 4, Horace Slughorn).
Slughorn has to spend his life on the road. Dumbledore could've offered him the protection of the Order if he'd wanted. Yet he leaves Slughorn very much to fend for himself. Slughorn was on his own throughout Order of the Phoenix, leaving the crucial information of the memory seemingly undefended. Dumbledore must have been confident that Voldemort wasn't going to target Slughorn or he would've offered him protection a year earlier. (It's true that Voldemort was operating in the shadows that year so assassinating Slughorn may have been risky. Nevertheless, it would surely have been a risk worth taking if the secrecy of the Horcruxes was at stake).
When Slughorn does belatedly decide that he would benefit from Dumbledore's protection it is again a lack of loyalty to the Death Eaters which he thinks may make him a target, not the memory.
“Well, yes, it is true that He-Who-Must-Not-Be-Named has never sought a fight with Dumbledore,” he muttered grudgingly. “And I suppose one could argue that as I have not joined the Death Eaters, He-Who-Must-Not-Be-Named can hardly count me a friend...in which case, I might well be safer a little closer to Albus...I cannot pretend that Amelia Bones’s death did not shake me...If she, with all her Ministry contacts and protection...”
It therefore seems likely that Voldemort deemed that Slughorn would never disclose the memory to anyone, and acted accordingly by leaving Slughorn alive. Dumbledore did believe that Slughorn would share the memory under the right circumstances but judged correctly that Voldemort wasn't a threat to Slughorn because of the memory (even if he might have wanted to recruit Slughorn for other reasons).
Voldemort never discussed Horcruxes with anyone other than Slughorn. He gained most of the information which he needed about Horcruxes from books and only approached Slughorn because he wanted to know what the books wouldn't tell him - what would happen if you made more than one Horcrux.