Bannan is not thought to be in Palace's first team plans, especially with the club signing former Wolves winger Bakary Sako in the past 24 hours, who adds competition to the midfield ranks.
Bannan can play centrally or out wide and his versatility could make him a coup for Championship sides.
Bolton could claim to have the biggest advantage, having signed Bannan on loan last season after Alan Pardew gave him permission to leave.
The Trotters however recently failed in their efforts to sign last season's loanee Adam Le Fondre, due to a lack of finances, and have re-signed 37-year-old Emile Heskey instead.
Leeds United have been looking for wingers all summer, and bought Stuart Dallas from Brentford earlier this week. Derby could claim to give Bannan the clearest shot at promotion, but he would have to dislodge Tom Ince to get into the first team.
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Bannan played 16 games last season, creating an impressive 43 chances, which led to three assists.
The Mirror reported last month how Bannan was not included on Palace's pre-season tour to South Africa, claiming newly promoted Norwich City were interested, but the Canaries have since signed Hull City's Robbie Brady instead.