Celtic are set to begin formal negotiations with Quinton Fortune within 48 hours.
The South Africa international was released by Manchester United this summer after failing to hold down a regular first-team place at Old Trafford following a knee injury.
The 29-year-old utility player was at Celtic Park on Friday for an informal meeting with Hoops' boss Gordon Strachan.
Fortune is also being courted by Bolton and Manchester City but the player's agent, Francis Martin, told PA Sport is hoping to begin more serious discussions with Celtic chief executive Peter Lawwell on Thursday.
He said: 'Hopefully, we will speak to Peter Lawwell on Thursday.
'The meeting is not 100% set-up yet, but we hope that's when we will be speaking to Celtic.
'We don't know if they will make an offer straight away, but, hopefully, we will begin talks.
'Celtic's interest is clear, we were invited up for an informal chat last Friday. But Quinton is keeping an open mind on things.
'We have to make sure everything is right from a financial point of view and also from a football point of view, especially from the football side of things because Quinton just wants to play regularly again.
'He has been injured so his priority is to get fit for the pre-season and play first-team football on a regular basis.
'If an offer is on the table, then he will have to decide whether he wants to stay in the north-west of England or a clean break and try a new league altogether.
'I will sit down with Quinton and his wife and he will have a decision to make.
'But I can't really say whether Quinton is leaning towards Celtic or not, there are plusses there but there are plusses at other clubs who are interested.'
Meanwhile, Michal Kadlec's representative, Pavel Zika, insists negotiations are on-going with the Hoops despite a reported disagreement over the fee for the 21-year-old Sparta Prague defender.
Zika told Czech Republic newspaper, Sport: 'Celtic's interest is the strongest and it is not unlikely things will start moving during this week and the transfer will be realised.
'We will talk with the representatives of Celtic in the coming days.'
Kadlec also reiterated his desire to play for the Bank of Scotland Premier League champions.
He said: 'The offer from Celtic pleased me and I think that every footballer wanted by such a club would be interested in playing for them.
'Celtic means a great atmosphere, superb fans and a sold-out stadium all the time.'
Sparta spokesman Lukas Pribyl is waiting for the Hoops to follow up on their initial interest in Kadlec.
He said: 'It is true that Celtic have been interested in signing Kadlec, but there has been no progress in this matter.'