The 25-year-old has been placed on the transfer list after rejecting a new deal at Elland Road and he has been linked with Newcastle, Middlesbrough, Barnsley and Doncaster.
Beckford scored 34 goals in 2008/09, but Leeds again failed to secure promotion from League One and their star forward is understood to be keen to play at a higher level.
However, Beckford's representative insists the player will not join a club that does not meet his aspirations and has indicated that the forward would be ready to run down the remaining 12 months of his Leeds contract.
Agent Nick Ruberry said in the Daily Mirror: "Jermaine won't consider anything other than a top-end Championship club or a Premier League club because Leeds are still a huge side.
"If he needs to, he will stay at Leeds for another 12 months."