The 18-year-old has caught the eye at Parkhead after scoring five times in 17 games so far this season for Dinamo Bucharest.
Though United have been strongly linked with an interest, his father says the only offer so far has come from Celtic.
"Celtic were the first team to come up with a concrete offer for Dorin, but they were refused," said Elijah Rotariu. "I don't know whether they will make any new proposal for him."
The teenager claimed earlier this month that he had spoken to Old Trafford officials in Bucharest. "We chatted for around two hours," he said. "When a club the size of United has you in sight, you can only be proud."