Carrick replaced Ruben Amorim in January and has won seven of his ten Premier League games, with two draws and one defeat — a 2-1 home loss to Leeds on Monday his only setback. United remain third and well placed to secure Champions League qualification with six games remaining.
Vidic was at Old Trafford for the Leeds match and spoke in glowing terms about the man he played alongside for nine years.
"He's a great character, a strong character but obviously in a different way," the former Serbia international said. "He's very knowledgeable, very calm and you can always rely on him."
The 44-year-old defender was equally emphatic about Carrick's suitability for the role. "He's not the guy who is going to have many days up and down, he's always going to be in the same line and you can see the way he is in the games and how he's presenting the club in the media. This is the manager you want to have in the club, because he's the face of the club."
Vidic pointed to the results as the clearest argument. "I think he represents the club in the best manner, plus he got the results — seven wins in 10 games, two draws and just one game lost. That's a fantastic record, plus I believe the players are enjoying it and taking the best out of it."
Reports suggest Carrick is now firmly in contention for the permanent position, with Julian Nagelsmann the only other serious candidate currently in consideration. Carrick himself has been measured on the subject, saying the club must make the right long-term decision and that his focus is solely on finishing the season strongly.
His opening win as United manager — a 2-0 derby victory over Manchester City on 17 January — set the tone for a turnaround that has shifted the mood significantly at Old Trafford. Vidic was in the stands for it. "I'd not felt Old Trafford with that energy and passion for a long time," he said.