The Red Devils have been linked with a move for the experienced free agent, who is looking for a new club following his brief ill-fated spell with Notts County.
While some have questioned whether the former England international still has what it takes to succeed in the Premier League, Redknapp has no doubts of his qualities.
Redknapp concedes the defender regrets his Magpies move but reckons he would be a short-term success for United.
"Campbell can prove, as Swedish star Larsson did, that he still has the quality to play at the very highest level and I'm not surprised at the reports tipping him for a Premier League return.
"Not too many people took to the idea of striker Larsson doing a more than decent job for Alex Ferguson back in January 2007 when he was plucked from Swedish part-timers Helsingborgs.
"United went on to win the Premier League title that season, two months after Larsson, now 37, went home to Sweden with Sir Alex full of praise for the way he handled himself."