The stand-off is reportedly attracting interest from French club Racing 92, having been linked with Toulon, Montpellier, Bath and Gloucester in January.
Speaking to BBC Scotland, Rennie said: "I've really enjoyed working with him so far. I think he could be something really special. We'll do our best to keep him."
While French magazine Midi Olympique reports an annual salary for Russell of 450,000 euros should he move to Paris next summer, Rennie said that if the player remains in Scotland "it certainly won't be for the sort of money you're talking about over in France".
"He just needs to consistently perform like he did last week," said the New Zealander, referring to Russell's man-of-the match display against Munster at Scotstoun in the PRO14.
"But in the end it's a professional sport and you do what's best for you and your family.
"Hopefully, Scotland can rally round him and keep him here."
Russell broke his nose in the 37-10 victory over the Irish and is being rested for Friday's home match against Benetton.
"He's fine," was Rennie's assessment.
"He could have played this week but we've got to rest him over the next week or so and we're pretty keen to put a strong side on the field against Cheetahs [away, PRO14, 6 October], based on the fact we have Exeter the following week [away, European Champions Cup, 14 October], so we decided to rest him this week."
Rennie, meanwhile, intimated that he expects lock Jonny Gray to be fit for the trip to Africa to play Cheetahs and that full-back Stuart Hogg is a few weeks away from a return, most likely against Leinster at Scotstoun in the European Champions Cup on 21 October.