In the original theatrical release of Star Wars, Boba Fett does not appear. In the behind the scenes though, I recall Jabba was originally filmed (as a human, not a slug), and then the scene was cut. The scene was restored in the Special Edition, with the human replaced with the slug. Was Fett a part of that originally cut scene, or was he specifically added to the Special Edition?
There is no mention of Boba Fett specifically in the shooting script, only "a half dozen grisly pirates and purple aliens":
INT. DOCKING BAY 94 - DAY Jabba the Hut and a half dozen grisly pirates and purple aliens stand in the middle of the docking bay. Jabba is the grossest of the salivering hulks and his scarred face is a grim testimonial to his prowess as a vicious killer. JABBA Come on out Solo! A voice from directly behind the pirates startles them and they turn around to see Han Solo and the giant Wookiee Chewbacca standing behind them with no weapons in sight. HAN I've been waiting for you Jabba. JABBA I expected you would be. HAN I'm not the type to run. JABBA (Fatherly-smooth) Han, my boy, there are times when you disappoint me ... why haven't you paid me? And why did you have to fry poor Greedo like that ... after all we've been through together. HAN You sent Greedo to blast me. JABBA (Mock surprise) Han, why you're the best smuggler in the business. You're too valuable to fry. He was only relaying my concern at your delays. He wasn't going to blast you. HAN I think he thought he was. Next time don't send one of those twerps. If you've got something to say to me, come see me yourself. JABBA Han, Han! If only you hadn't had to dump that shipment of spice ... you understand I just can't make an exception. Where would I be if every pilot who smuggled for me dumped their shipment at the first sign of an Imperial starship? It's not good business. HAN You know, even I get boarded sometimes, Jabba. I had no choice, but I've got a charter now and I can pay you back, plus a little extra. I just need some more time. JABBA (To his men) Put your blasters away. Han, my boy, I'm only doing this because you're the best and I need you. So, for an extra, say ... twenty percent I'll give you a little more time ... but this is it. If you disappoint me again, I'll put a price on your head, so large you won't be able to go near a civilized system for the rest of your life. HAN Jabba, I'll pay you because it's my pleasure.
So a character like Boba Fett is certainly a possibility for this scene, but the character does not seem to have been specifically planned at this stage.