"No one has come in for Sam. At the moment he's with us and is in our Champions Cup squad. We're not in negotiations with anyone. Leeds haven't been in contact with me.
"It's resolved at the moment. Sam is contracted with us. As far we're concerned he's with us and will continue playing for us."
After just one season in the game, Burgess was selected at inside centre for England during the World Cup, starting the loss to Wales and making replacement appearances against Fiji and Australia, but played his best rugby for Bath last season at blindside flanker.
Craig insists blindside flanker is his natural home and is convinced he would have been more advanced in his union apprenticeship had be spent the summer with the club learning his trade instead of being picked by England.
"We brought Sam over with a specific brief, which was that he'd play in the back row," Craig said.
"That's where he'll play for us. That's where we see him and where his best qualities are and where Sam sees himself.
"If he wasn't picked in the England squad, obviously his development would have increased.
"I'm absolutely sure he can be a star of the World Cup if he sticks around. I think he can be a great number six."
Coach Mike Ford revealed that Bath are in the market for a new back row and he can ill-afford to lose Burgess with a punishing run of Premiership and Champions Cup fixtures looming.
Once London Irish have been negotiated, appointments with Toulon, Leinster, Leicester and Northampton, followed by a double header against Wasps, take care of the schedule until Christmas.
Ford hopes the succession of big games will revive Burgess' appetite for the game.
"For a player to have that hype around him at a home World Cup and then have massive disappointment, when is that going to clear in his mind?" Ford said.
"We just want Sam to be Sam and that means him carrying the football and making tackles. We believe he does more of that when he is at six.
"We have some really juicy fixtures coming up and knowing Sam as a competitor, he will want to play in those games and if he plays well it will help him."
Captain Stuart Hooper has acted as a sounding board for Burgess following his return from a 10-day break in Spain with his partner Phoebe Hook.
"Sam came back in on Monday, came back into the changing room and it was the same old banter. He's been fantastic," Hooper said.
"I had a sit down with him as captain. I care about all our guys, I care about them a lot. I just wanted to say to him I'm here and I want to help you.
"He has had a lot of stuff written about him and a lot of stuff written about his fiancee.
"When he is in our changing room he is a fantastic bloke, enjoying being with us and wanting to be with us."
