Wellens this week reached a settlement with the Foxes over the remaining year on his contract at the King Power Stadium and is now a free agent.
All summer the 33-year-old has been linked with a return to Rovers, for whom he helped win promotion to the Championship and made almost 100 appearances between 2007 and 2009.
Doncaster boss Paul Dickov would like to offer Wellens a contract but the South Yorkshire club's talks with potential investors are currently stalling his recruitment plans.
After being released by Manchester United in 2000 Wellens played for Blackpool and Oldham prior to his arrival at Doncaster.
In 2009 he joined Leicester but made just four appearances for the Foxes last season and was sent to Ipswich on a month-long loan as he recovered from a cruciate ligament injury.