The 26-year-old hit the headlines when he netted the goal which knocked Manchester United out of the FA Cup at Old Trafford, and then went on to score a dramatic equaliser against Tottenham with a stoppage-time penalty to earn Leeds a fourth-round replay.
Beckford took his tally to the season to 24 with a brace against League One promotion rivals Colchester last weekend.
"He did well and would be a good gamble for someone in the Premier League, I am sure someone will take him," said the Spurs boss ahead of Wednesday night's trip to Elland Road.
"He is a free at the end of the season, and someone has probably done a deal with him, rather than paying a couple of million for him now.
"They will wait and take him at the end of the season on a free."