The 25-year-old has 12 months remaining on his current deal but has turned down the chance to further extend his stay at Elland Road and could be free to talk to other clubs as early as January, possibly leading to a free transfer next summer.
Leeds chief executive Shaun Harvey told the club's official website: "As a policy, we will always look to retain our most effective players.
"However we will only do so within the financial parameters that we believe are appropriate. The offer we have made to Jermaine is what we believe to be a very good offer but he has exercised the 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 scored 34 goals in all competitions for Simon Grayson's play-off semi-finalists this term and has notched 54 times in 98 appearances since his arrival from non-league Wealdstone back in 2006.