Celtic had an initial offer of £900,000 for the 23-year-old knocked back earlier this week but Ronny Deila’s side have come back with an improved bid that has now been accepted.
Championship side Wigan Athletic have already had a bid in excess of £1m accepted by United but Ciftci’s representative says the striker is flattered by a club like Celtic’s interest in him.
Tannadice boss Jackie McNamara has said the final decision on where the 16-goal forward ends up will rest with Ciftci, who has just one year left on his current contract.
Former Celtic striker Pierre van Hooijdonk, who is representing Ciftci, said: “I know that there’s been an accepted offer from Wigan but Nadir has said no to that offer.
“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.”
The Tangerines released a statement on their official website which said: “Dundee United today confirmed that an undisclosed fee had been agreed with Celtic for Nadir Ciftci and permission has been granted for the Glasgow club to speak to the player.”