Beckford, who scored 34 goals for Leeds last season, is 12 months away from the end of his existing deal and now looks likely to leave Elland Road this summer.
Chief executive Shaun Harvey said: "The offer we have made to Jermaine is what we believe to be a very good offer, but he has exercised his right to turn it down.
"On the basis that he has 12 months remaining on his current contract and could leave on a free transfer next summer, we feel we must consider any offers that are forthcoming for him. In the event that no offers are forthcoming or the offers received are unacceptable to us then he will remain part of Simon Grayson's squad next season."
Beckford has had loan spells at Carlisle and Scunthorpe, helping the Iron to promotion to the Championship in the 2006/07 season.