Wellens' current deal expires at the start of January and as yet there have been no talks over an extension.
The 33-year-old has established himself as a key figure for Paul Dickov's side since arriving on a free transfer in the summer and was the stand-out performer in the recent win over high-flying Queens Park Rangers.
Wellens, who has made 18 appearances for Rovers this season, was persuaded to sign a short-term deal in September by Dickov and former chairman John Ryan.
The midfielder, who is in his second spell at Rovers, is a big fans' favourite at the club and was recently named skipper by Dickov.
However, sources close to Wellens believe the player has been left concerned by the club's failure to secure new investors despite months of talks over a possible takeover and the departure of father figure Ryan from the Keepmoat Stadium.
Should Rovers fail to secure Wellens on a new deal there is sure to be no shortage of suitors, with the former Leicester man widely regarded as one of the best midfield playmakers in the Championship.