The striker is on the transfer list and has been linked with interest from City and now Middlesbrough.
However, there has only been one firm bid on the table and that has come from a League One club.
Beckford's agent Nick Rubery told the YEP: "On the basis that we've had one offer and he's now on the transfer list, it seems pretty likely that he'll be leaving before next season.
"It's a good offer from a League One club but the increase in wage was so insignificant that it gave us nothing to think about."
http://www.yorkshireeveningpost.co.uk/sport/Leeds-United-The-race-for.5304864.jp