Former midfielder Wellens returned to Rovers in the summer following his release by Leicester but the short-term deal he signed expired after the league defeat at QPR on New Year's Day.
Manager Paul Dickov is confident the 33-year-old will sign a new contract, despite strong interest in the player from rival Championship clubs.
Baldwin released a statement via the club's official website on Monday afternoon to set the record straight about Doncaster's negotiations with the out-of-contract midfielder.
"Paul Dickov has expressed a desire to keep Richie and the owners have backed him," said Baldwin.
"After long discussions with the player over a period of time we've offered Richie a contract.
"It's fair to say that the length of the contract could be considered long term for a player of his age and beyond the usual length we offer to a player over 33. We're hopeful he will sign.
"Richie keeps saying he wants to stay and we've offered a deal beyond our usual parameters, based purely on his performances this season.
"Paul's regularly repeated his admiration of him, so ultimately everything we can do has been done."
QPR have been linked with a move for Wellens while Leeds are also rumoured to be interested.