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 former top-flight clubs Newcastle and Middlesbrough.
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.
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."