Wellens, who made almost 100 appearances for Rovers between 2007 and 2009 and helped them win promotion to the Championship, has been training with Paul Dickov's side since having his contract with Leicester cancelled by mutual consent last week.
It is understood that a longer deal is on the table for the 33-year-old provided there is a successful conclusion to the investment talks currently taking place at the South Yorkshire club.
Wellens becomes the fourth player to join Doncaster this week following the arrivals of Bongani Khumalo, Ross Turnbull and Harry Forrester.
After being released by Manchester United in 2000, Wellens played for Blackpool and Oldham prior to his arrival at Rovers.
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.