The Serbian signed for the Red Devils from Spartak Moscow in 2006, but Carragher has admitted that he would have "loved" to have played alongside Vidic at Anfield.
"[Vidic is] my type of defender. Liverpool tried to buy him in January 2006 but our loss was United's gain. I'd have loved to have played alongside him and I'm sure we could have formed a solid partnership," Carragher wrote in his Daily Mail column.
"He loves defending and putting his head in where it hurts. His arrival took [Rio] Ferdinand's performances up another level. They became the best defensive pairing in Europe."
Vidic left United during the summer for Inter Milan.