Vidic’s close friend and manager of Serbian side FK Vojvodina, Nenad Laltovic, revealed the offer and has encouraged him to take it up.
Laltovic told Elta TV: “Vidic lives in Milan and he is currently considering coaching, he is not yet sure. He was already offered to run Manchester United B.
“I told him, “this is an ideal opportunity if you want to do it – to go back to England, you’ll take over tomorrow and Manchester, you have a great name there and I think that’s the right decision for you.”
“But he has not decided yet. I’m supporting him being coach at Manchester United, as then there is a chance for him to take over the first team in the future.”
The job has been vacant since the end of last May when Ricky Sbragia left the club after the U-23s finished sixth in League Two.
The Old Trafford club have identified two other candidates for the vacancy with former midfielder Quinton Fortune also thought to be in the running.
Centre-half Vidic, 37, spent nine years at United between 2005 and 2014 winning five titles, three League Cups, the Champions League and World Club Cup.
He moved to Inter Milan for 18 months before retiring in January 2016.