The Mirror says former Birmingham and Aston Villa midfielder Gardner, 25, wants to return to the Midlands for family reasons.
He has struggled to settle in the North East and has Albion, Wolves and Villa all interested after scoring 10 goals last term.
But the Baggies are now favourites to get Gardner on an initial loan ahead of a permanent transfer.
Albion like Gardner and are willing to then offer him a three-year deal next summer.
But they spent all of their 2011/2012 transfer budget this summer and cannot afford to buy him outright now.