Thomas Gravesen's agent John Sivebaek claims the player is mulling over a move to Celtic.
Manager Gordon Strachan is said to have identified the Real Madrid midfielder as his priority transfer target.
Sivebaek says only 'three or four' clubs are left in the running for the signature of the 30-year-old, who has been told he is surplus to requirements at the Bernabeu.
He told the Daily Record: 'We are still in talks with these clubs but hopefully something will be finalised in the next week, perhaps even sooner.
'Thomas is still warm on the idea of moving to Glasgow because it is such a big club.
'Of course, for most players the idea of playing in the English Premiership is more interesting than the Scottish league but Celtic will be in the Champions League this season and that's very attractive for Thomas.'
Newcastle are one of the clubs thought to be battling it out with Celtic for a player who was a huge success during his time in England at Everton.
Gravesen's wages - rumoured to be in excess of £80,000 a week in Spain - would cause a stumbling block.
Sivebaek added: 'Real Madrid have told us they will look very positively at whatever offer they receive. I've heard a rumour the price they want is £2million.'