United were thrashed 6-1 at home by Tottenham on Sunday, having begun the season with a shock 3-1 loss to Crystal Palace.
Former United captain Keane feels the club’s players were culpable in Jose Mourinho’s departure from the Old Trafford dugout in December 2018 and fears his ex-team-mate Solskjaer will suffer a similar fate.
“The performance against Spurs was disgraceful… we’ve all been in football, we’ve had bad days, but I thought it was a disgrace to the badge, some of the players’ performance,” Keane told ITV.
“Too many bluffers, and ultimately I think they will cost Ole his job.
“They threw the previous manager (Mourinho) under the bus, they will do exactly the same to Ole.”
Under-pressure Solskjaer confessed the humiliation at the hands of Spurs was his worst day in football.
Ten-man United sunk to their joint heaviest Premier League defeat as Mourinho returned to haunt his former club in emphatic fashion.
Gary Neville, a former United team-mate of Solskjaer and Keane, had already described the debacle as “an absolute shambles” as United matched a 6-1 loss to Manchester City in 2011.