Riordan is seeking a move away from Celtic after growing increasingly frustrated with his lack of first-team opportunities.
The 24-year-old has only started 12 games in all competitions since arriving at Parkhead from Hibernian in the summer of 2006.
Riordan expressed his desire to find a new club last week and the news has alerted a number of clubs to the forward's possible availability.
Celtic are thought to be willing to listen to offers for Riordan as Gordon Strachan says he does not want unsettled players at the club.
The duo could now rekindle their interest in the talented forward and make a move for his signature when the transfer window reopens in the New Year.