The Croatian feels the Bundesliga champions, German Cup winners and Champions League finalists would benefit significantly from signing the Red Devils' defender.
Speaking to Sport Bild, Olic said: "When I heard Bayern were aware of him as a player I told him to join our club and get to know a different sort of league.
"He is definitely under contract at one of the best clubs in the world and he is absolutely one of the best defenders in England."
Vidic has been linked with a move away from Old Trafford in the past, with both Real Madrid and Barcelona reported to be interested in luring the Serbian international away from Sir Alex Ferguson's side.
But Olic, who scored in both legs of Bayern's recent Champions League quarter-final victory over United, feels the Serbian - who has made more than 120 Premier League appearances for the Red Devils - should head to Germany.
"If he is really eyeing a transfer, Bayern should be a serious contender," he said.
"I am always telling him down here in Munich life is beautiful for you and your family."
By Owen Edwards
