The 24-year-old has not entirely convinced fans he is worth the £89m transfer fee paid to Juventus last summer.
But Robson is convinced Pogba will eventually prove himself to be one of the finest midfielder in the world and that Mourinho may make him captain.
“Mourinho will make that decision regarding who’s captain,” Robson told Sport Witness. “But once Paul Pogba is settled into the club again, gets used to the Premier League again, as long as he keeps improving, I think he’s captain material.
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“I think Paul works really hard at his game. I think he wants to be one of best, if not the best midfielder in the world, so he’ll keep working at it, keep improving and become a real bright player for Manchester United.”
After starring for Juventus in the Champions League final in 2015, Pogba could go two years without playing in Europe’s premier competition.
United are four points off the pace in the hunt for a top four finish and may have to win the Europa League to qualify through the back door.