The Reds failed to offload Wilson during the international transfer window as they could not find any takers for the winger, who they value at £20m.
The domestic transfer window is still open for business and a host of Championship sides are showing interest in snapping him up.
Swansea have been in pole position due to their handling of Rhian Brewster on loan last season, but while the Welsh giants have made a move for Wilson, it has been knocked back.
It is claimed that financially the deal was a non-starter for Swansea and the club now look to be out of the race.
Now Derby are favourites to snap up Wilson, though the Rams do not have an agreement in place with Liverpool.
Liverpool will be keen to let Wilson leave on financially advantageous terms, as well as picking the right destination from a footballing perspective.
The clock is ticking on the domestic transfer window and it remains to be seen where Wilson ends up.