Having held preliminary talks with representatives of Sheffield United in early December, Newcastle officials made fresh contact with Bramall Lane chiefs yesterday to lodge a formal bid for Kilgallon.
The Magpies are understood to have offered an initial down payment of £1m for the former England Under-21 international, with additional fees dependent on the player's performance and the club's potential promotion to the Premier League.
Blades chairman Kevin Mc- Cabe has insisted Kilgallon will not be allowed to leave on the cheap this month, despite his current contract expiring at the end of the season.
However, manager Kevin Blackwell is resigned to losing the services of the centre-half, and is already targeting possible replacements.
Tellingly, Blackwell substituted Kilgallon at half-time during his side's FA Cup draw with QPR at the weekend, in order to prevent further damage to a tight hamstring that could have scuppered any prospect of a quick move.
Celtic have also been monitoring Kilgallon's situation as they line up a successor to Gary Caldwell, who is expected to leave Parkhead for Middlesbrough.
But the Bhoys will be unable to match Newcastle's wages and sources in Yorkshire claim Kilgallon is keen to move to St James' Park.
The former Leeds United defender has refused to sign a new deal with Sheffield United on a number of occasions, and is hoping to earn a return to the Premier League with the Magpies.
He could yet be joined by Beckford, but having spent the second half of December attempting to pave the way for a quick deal at the start of this month's transfer window, Newcastle now face a protracted battle to secure the striker's services.
While Leeds boss Simon Grayson delivered a bullish assessment of his side's chances of holding on to Beckford in the wake of Sunday's surprise 1-0 win at Manchester United, others close to the Elland Road club still expect the 26-year-old to leave West Yorkshire this month.
Whether Beckford ends up at Newcastle, though, is a different story, with Wigan and Stoke also lining up moves.
The Magpies had a £1.25m bid rejected last week and that has opened the door for other suitors.
With Beckford having confirmed his qualities with Leeds' match-winner at Old Trafford on Sunday, Premier League clubs are now preparing to enter the fray.
Wigan boss Roberto Martinez has been promised cash to spend this month as he attempts to keep his club in the Premier League, and Beckford is understood to figure prominently on his list of targets.
Stoke manager Tony Pulis is also targeting strikers, and while Sunderland's Kenwyne Jones continues to be an option, Beckford is also believed to feature on his wanted list.
As a result, Leeds officials are likely to wait as long as possible before accepting a bid, who is out of contract in the summer, but Newcastle boss Chris Hughton is prepared to play a waiting game.
We have to be patient and there is a long month ahead of us, but we won't panic,
said Hughton. I wasn't at Old Trafford to see Jermaine and there is no deal done yet.
All we can say is that we're working very hard on bringing in players and I am very confident we will get them.
His profile now goes up because the game was on TV.
But everybody knows that this is just one game and whether he'd done well or badly, he would still be a talented player.
Meanwhile, Newcastle have refused to confirm Geremi's move to Ankaragucu, despite the midfielder being paraded in front of the Turkish club's fans yesterday.
Ankaragucu officials claim to have signed Geremi on an 18-month contract, but Magpies officials were taken by surprise by the internet announcement late on Sunday.
A club statement last night read: Newcastle United wishes to make it clear that whilst there are a number of clubs interested in possibly acquiring his services, any talk of him leaving St. James' Park at this moment is extremely premature.
Geremi remains a Newcastle United player and has today linked up with Cameroon for the African Cup of Nations.'' Newcastle's FA Cup thirdround replay with Plymouth Argyle has been confirmed for Wednesday, January 13 (ko 7.45pm).
Tonight's home reserves game with Scunthorpe United has been postponed because of a frozen pitch at Whitley Park.