Sky sources understand a bid of around £900,000 was submitted by the Parkhead side for the Turkish-born forward, who scored 16 goals last season.
United are thought to value Ciftci at more than that and it is unclear whether Celtic will return for another offer for him.
Collins was guarded when asked about the 23-year-old but conceded he is a player he and the SPFL Premiership champions’ manager Ronny Deila admire.
Speaking to Sky Sports News HQ, he said: “I believe there is an approach but that’s all I’ve heard and there’s not a lot I can tell you.
“He has obviously played against us many times last year, he’s a big striker, he’s strong, he’s powerful and he’s got technique as well. We like him.
“We’re looking to strengthen the squad but unfortunately we can’t talk about other players at other clubs. It would be unfair and disrespectful to the other clubs to do that but we are looking for new players.
Collins and Deila will see Celtic play for the first time this summer when they host Dutch side Den Bosch on Wednesday at St Mirren Park in Paisley.
But they will have to do without forward Kris Commons, who has been sidelined after breaking a toe when a wardrobe door fell on him.
Although he hasn’t been able to train fully, he has been working in the gym and Celtic remain hopeful he will be fit for their first Champions League qualifier with Stjarnan on July 15.
Otherwise, there are few injury problems but Collins concedes many of Celtic’s players might not be as fresh as he would like due to their seasons only finishing a couple of weeks ago.
He added: “I think we’ve got nine international players who have just had a fortnight off. The reality of modern-day football is it’s a sign of success when you play for your country.
“The international matches go into the close season and eat into holiday time but the players have to deal with that.
“As coaching staff and a medical team, we just have to deal with that and manage them when they come back.
“We need to make sure they get enough days off while at the same time keeping their sharpness up. The boys are looking forward to getting back started.”