The former Everton and Birmingham forward impressed during a short spell back at his first club Motherwell during the second half of the 2012/13 season.
The 28-year-old scored five goals in 13 appearances for the Fir Park outfit but is now a free agent again after his deal expired at the end of the campaign.
Stuart McCall's side are believed to be keen on a permanent deal for the player but face competition from SPL rivals Celtic.
The Scottish champions have been long-term admirers of the Scotland international and now look set to convert that interest into a concrete offer.
However, a number of English clubs are also believed to be planning moves to hijack the deal and bring McFadden back south of the border instead.