Magpies chiefs made a firm approach earlier this week in an attempt to tie up a deal before the transfer window officially reopens tomorrow morning.
Having tracked 26-year-old Beckford for the best part of two seasons, Newcastle officials finally made formal contact with their counterparts at Elland Road and offered £1.25m for the striker's services.
While the London-born forward has scored 19 goals in 27 appearances this season, Magpies owner Mike Ashley is reluctant to pay much more than that for a player who is out of contract in the summer, and would therefore be available for nothing in June.
Ashley is also understood to feel that Beckford's lack of Premier League experience should mitigate against a higher fee.