The 2005 Lions tourist was suspended for two years in January 2009 after admitting to taking cocaine.
Stevens is currently unable to have any involvement in rugby until January 2011 and his career in the sport had been questioned by many critics at the time of the controversy.
But after former Lions hero Lawrence Dallaglio admitted London Wasps would happily give the 27-year-old a lifeline in just over a year's time, Bath have made their own position clear by stating that they too wish to resign Stevens.
"I have spoken to Matt about where he sees his future and what he would like to do," said new Bath chief executive Nick Blofeld.
"We would love him to come back to us and I have made that clear."
Bath have struggled for form this season and Bloefeld believes Stevens' absence has played a part in their poor run of results.
The South African-born prop was expected to challenge for a place on the 2009 Lions tour of his home country before his high-profile exit from The Rec and Bloefeld is certain that Stevens can return to the kind of form that made him one of Europe's most-promising front rowers, despite his lengthy lay off.
"I may not have been at the club for very long, but in that time it is clear that Matt's presence has been missed both on and off the pitch," added Bloefeld.
"He is a big character with strong leadership skills and a lot of charm.
"It therefore came as a shock to everyone when the news broke and we had no precedent when it came to dealing with it.
"Matt has kept very fit and has even become a Brazilian Ju Jitsu champion, which is an extraordinary feat and demonstrates again his drive and determination to succeed."
As for Stevens himself, he too has stated that being offered a return to The Rec is hugely promising.
But, with Wasps already throwing their hat into the ring and other clubs now likely to do the same, Stevens remains noncommittal on his future.
"I'm very pleased that Bath have spoken to me and said they would like me to come back," admitted Stevens.
"It is obviously early days for my future rugby career but Bath and the rugby club are obviously still a big part of my life and I will give it very serious consideration."