Carragher believes the likes of Pep Guardiola, Jurgen Klopp and Chelsea boss Thomas Tuchel would win the Premier League title with the current squad at Old Trafford.
Despite being backed in the transfer market, Solskjaer is yet to win a trophy since he was given the top job at Old Trafford in December 2018.
He has overseen the signing of players like Harry Maguire, Bruno Fernandes, Alex Telles and Donny Van de Beek among others in the previous transfer windows.
The Norwegian has also been backed this time around with the signings of Jadon Sancho and Raphael Varane.
Manchester United legend Gary Neville suggested that the club should go in for want away Tottenham Hotspur striker Harry Kane in order to be able to mount a title challenge but Carragher does not agree with his compatriot.
“The answer is always go and spend £100million on someone. Go and blitz the transfer market,” Carragher said.
“You talk about Chelsea buying Romelu Lukaku and people say they’re going to win the league – it’s them or City. Manchester United finished above them last season and they’ve bought Raphael Varane and Jadon Sancho!
“I don’t get this feeling that Manchester United can’t compete. If Pep Guardiola, Jurgen Klopp or Thomas Tuchel had Manchester United’s squad, they could win the league.”