Championship sides Coventry City, Middlesbrough, Newcastle, Sheffield United, Doncaster, Barnsley, Peterbrough and Scunthorpe have all been linked with the former Wealdstone player.
However, his agent Nick Rubery has said that he is only interested in receiving offers from the top clubs in the country.
Everton are one top flight club reported as being interested in Beckford has turned down a new deal at Elland Road and has a year left on his contract.