The Scottish champions’ advances have so far been turned down, with United stating their preference is to sell the Turkish-born forward to a club in another country.
While Celtic’s initial offer of £900,000 was knocked back earlier this week, Wigan Athletic later had their bid in excess of £1m accepted.
Ronny Deila’s side then came back with an enhanced bid but it was once again thrown out, while the player is reportedly not satisfied with the terms Wigan have presented.
Dundee United manager Jackie McNamara has said the final decision on where the 16-goal forward ends up will rest with Ciftci himself if Celtic come back with an agreeable price.
It appears remaining in Scotland could be his favoured option with his agent, former Celtic striker Pierre van Hooijdonk, keen to conclude discussions.
“I know that there’s been an accepted offer from Wigan but Nadir has said no to that offer,” said the Dutchman.
“Celtic have been in touch with two bids but those have been rejected by Dundee United and that is the status at the moment.
“He is flattered by Celtic’s interest but that is quite normal when you realise the size of the club. Anyone would be interested.
“Our relationship with Dundee United is a very good one and we want to keep it that way. We will just wait and see what happens over the next few days and weeks.
“At the end of the day the player always decides what happens in my opinion. But we are not having a big argument with Dundee United.”