The Bhoys' previous bids of £900,000 and £1 million were rejected by United, according to the report, but the Glasgow outfit remain keen on acquiring the services of Ciftci.
English League One club Wigan Athletic are also interested in the Turkish forward, according to The Daily Record, but the player himself is claimed to favour a move to Celtic due to possible Champions League football next season.
Former Celtic striker Sutton has backed the club’s move for the former Portsmouth man and wrote in The Daily Record: “Recruiting a striker is the hardest position to conquer as the good ones cost so much.
“So it comes down to finding a project and Ciftci is at a good age for the club to develop his potential. As a footballer player, he has a lot going for him.
“He uses his body well, he can score different types of goals, he can bring others into the game and he can be a right handful…
“Also, Deila likes to play that centre-forward position as a lone task and he can do that really well from what I’ve seen.”
Ciftci is one of the best strikers in the Premiership and has been in brilliant form for the past two seasons.
In the 2013-14 campaign, the former Turkey Under-19 international scored 17 goals and in 2014-15 he found the target 16 times.