Probably because Saruman considered Gandalf's Ring useless to him. Elrond says of the Three Rings generally:
[T]hey were not made as weapons of war or conquest: that is not their
power. Those who made them did not desire strength or domination ...
but understanding, making, and healing, to preserve all things
from "The Council of Elrond" in "The Fellowship of the Ring"
At the time he gave it to him, Círdan the Shipwright tells Gandalf about Narya specifically:
For this is the Ring of Fire, and with it you may rekindle hearts in a
world that grows chill.
from "The Tale of the Years", Appendix B to "The Return of the King"
Círdan's words suggest that Narya's most important power (or at least its power that would be most important to Gandalf) is an ability to awaken hope and the will to survive in the hopeless.
No doubt its power was at work when Gandalf and the knights of Dol Amroth rallied the spirits of despairing Gondorians during the siege of Minas Tirith.
Saruman, as Middle-earth's second greatest authority on the Rings of Power, would have known all this; and known, too, that the Three Rings of the Elves "endure no evil", as Gandalf says to Frodo. Perhaps this last consideration carried weight with him. His words to Gandalf
We can bide our time, ... deploring maybe evils done by the way, but
approving the high and ultimate purpose: Knowledge, Rule, Order
from "The Council of Elrond"
show that he is aware that he is doing evil, whether or not he still deceives himself that good is his ultimate aim.
Treebeard characterizes Saruman thus:
He is plotting to become a Power. He has a mind of metal and wheels;
and he does not care for growing things, except as far as they serve
him for the moment.
from "Treebeard" in "The Two Towers"
Saruman's attempt to desolate The Shire seems to bear out Treebeard's description. Making, healing and understanding are not high on his priority list.
In any case, Saruman hoped for either of 2 outcomes from capturing Gandalf:
- If Sauron triumphed, to use the power of his Voice to become the power behind Sauron's throne.
- To use the One Ring to crush Sauron and become ruler of Middle-earth in his own right.
Saruman knows that even with the Ring of Fire, Gandalf is no match for Sauron, and Saruman probably wouldn't be either. Even with the ring it can't help him defeat Sauron.
The Ring of Fire also likely wouldn't help him manipulate Sauron; and in the event of Saruman becoming Sauron's servant, there would be a very real danger of Sauron discovering that his new adviser possessed one of the Three Rings -- with probable bad consequences for Saruman and his plans.