Campbell is reported to be a shock transfer target for United as they look to ease their defensive injury crisis and the former Arsenal, Portsmouth and England defender told ESPN Soccernet on Wednesday that he would leap at the chance to move to Old Trafford.
Parallels have been drawn with United's signing of Larsson in January 2007 when the Swede was captured on loan from Helsingborgs for two months and scored three times in 13 appearances, earning a Premier League medal in the process.
Redknapp, who managed Campbell at Portsmouth, feels that the 35-year-old could be a similar success if Ferguson does opt to sign the player who has not played a professional game since his one and only appearance for League Two Notts County in September.
"Sol Campbell can do at the back what Henrik Larsson did up front for Manchester United two years ago," Redknapp told the Sun. "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. Sir Alex needed a temporary fix for his squad when he was struggling with injuries to strikers Alan Smith and Ole Gunnar Solskjaer.
"With United now having problems with the fitness of key defenders like Jonny Evans, Rio Ferdinand and John O'Shea, it has a familiar ring about the Larsson situation to it.
"Sol can still do a job for anyone and probably the biggest mistake he has made in recent years was moving to Notts County. Not for one minute do I wish to disrespect anyone at Meadow Lane, I know they are honest pros who will do their best for the club.
"But one of the hardest things in football - and there are many - is trying to play alongside players who are not on the same level. That is the situation Campbell found himself in and while I don't know if he will go to Old Trafford, or if Sir Alex is interested, it would make sense."