Beckford still has six months of his current contract left to run and Leeds boss Simon Grayson has threatened to keep the player against his wishes if Newcastle refuse to up their offer.
Hughton, however, remains confident of signing the 26-year-old and is hopeful of securing two further players before the close of the transfer window.
There are plans to extend Danny Simpson's loan deal from Manchester United to the end of the season, with a view to a permanent switch, and the Magpies are also on the look-out for a defender after their failed attempt to sign Sheffield United's Matthew Kilgallon.
Hughton said: "We're not at the back end of the transfer window yet.
"In the ideal scenario you do your business as quickly as possible, but in most cases it doesn't tend to happen that way. That's the frustration this window brings.
"We'd rather do it nice and early, know what we have and go on from there, but that hasn't been the case.
"There comes a time when we will have to look elsewhere.
"I can't see us failing to sign anyone this month, in all honesty. What I wouldn't want to do is say categorically that won't happen, but I can't see it.
"I am still confident, very, very confident we will get the three players we want to add to the squad."
As things currently stand, Wednesday night's FA Cup replay against Plymouth will be the penultimate game before Simpson is due to return to Old Trafford and Hughton is remaining tight-lipped over negotiations.
"Any conversations between ourselves and Manchester United remain private," he added. "West Brom is Danny's last game. He has done very well and it is something we are working on.
"It is one of the areas we have consistently said we want to bring players in. Right-back, centre-back and centre-forward.
"Not necessarily different players, all the players we have brought in on loan have done very well.
"In Ryan Taylor we also have a player who has played a lot of games at right-back and some people think that is his best position."
Newcastle v West Brom To Win Both Halves: Newcastle 11/2