The 27-year-old striker has been the subject of interest from several clubs, of which Fulham are believed to be leading the chase.
Sky's report suggests that the Cottagers have come in with a second bid for the Leeds captain, while other clubs are still hopeful of landing his signature.
In other Fulham news, a man who used to play his football at Craven Cottage is set for a move to Roma.
TalkSPORT are reporting that 28-year-old Urby Emanuelson, who is now a free agent, will move to the Serie A side after his contract expired at AC Milan.
Stephane Mbia, Andrew Johnson, Aaron Hughes, Luke Young, Hogan Ephraim, Angelo Balanta and Tom Hitchcock have all left the club, while loan players Ravel Morrison, Benoit Assou-Ekotto, Tom Carroll, Nico Kranjcar, Will Keane, Kevin Doyle and Modibo Maiga have returned to their parent clubs.
A statement on QPR's website read: “Everyone at Loftus Road would like to take this opportunity to thank all of these players for their contribution to the club, and to wish them well for the future.”
However, Bobby Zamora, Rob Green, Armand Traore, Alejandro Faurlin and Gary O’Neil are all in talks over a new deal.