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The veteran German was appointed to oversee the side for the remainder of the season.
But he's been unable to influence the Red Devils, who languish in sixth place in the table - five points adrift of fourth-placed Arsenal.
Man United continued to look disjointed against Chelsea, but managed to gain a point at Old Trafford on Thursday.
After the 1-1 draw, Keane claimed his old side would be better off with the Norwegian in charge and slammed the decision to appoint a temporary manager.
🗣 "If Ole stayed on? In terms of the League position I'd say yeah."— Football Daily (@footballdaily) April 28, 2022
Roy Keane feels Manchester United would be in a better position if the club didn't sack Ole Gunnar Solskjaer pic.twitter.com/w5yZt3TtPp
Asked by Dave Jones if it was a mistake to relieve Solskjaer of his duties, the Irishman replied: "They wouldn't have done any worse if Ole was here.
"But obviously the decision was made, you can't keep looking back.
"You can go back to the other managers, go back as far as David Moyes. I'd always argue managers should be given more time than what they are but the reality of top football clubs is there's no patience."
Keane was then asked whether Man United would have been in a better position if Solskjaer stayed.
"If Ole stayed on? In terms of the League position, I'd say yeah," he replied.
"But you have to remember the last couple of games for Ole."
The 50-year-old also bemoaned the decision to appoint an interim manager.
"I'm not saying it wasn't time to go for Ole, but bringing in a temporary manager," he said before shaking his head.
Man United have just three games left of the season, with Erik ten Hag set to take over from Rangnick.