Solskjaer has been left stunned by the poor fitness levels of his squad since taking charge in December.
Now he has put them all on personal fitness regimes for the next six weeks and ordered them to report back to pre-season training ahead of schedule.
And Solskjaer has vowed to sell anyone who returns out of shape on July 1.
A United source said: “He was genuinely shocked at how unfit some of them were for top level professional athletes.
“He couldn’t do too much about this during the second half of the season.
“But he isn’t messing about. The players have been told to work on their fitness during the close season and those who look like they’ve ignored him will be axed.”
The bulk of United’s squad face an extended summer break due to the fact just a small number of them are expected to be involved in the Copa America.
Jesse Lingard and Marcus Rashford, meanwhile, are set to join-up with England for the UEFA Nations League semi-final against Holland in Portugal next month.
But the rest of the United squad have been challenged to come back for next season fitter than ever before.
Solskjaer is not messing about and knows he has to be as ruthless as possible if he is to make United great again.
The Norwegian has set the early return date in the hope of guaranteeing his players are fit enough to compete for the top four next season.
He subjected them to a tougher fitness regime after taking charge before Christmas that coincided with an upturn in results, with United winning 10 of Solskjaer’s first 11 games in charge.
But his fears United would suffer an adverse reaction in the final months of the campaign came true.
United collapsed, winning just two of their last 10 league games to finish outside the top four and fail to secure Champions League qualification.
United will play their first pre-season game of the summer against Perth Glory in Australia on July 13.
Solsjkaer has at least avoided the humiliating prospect of having to start United’s Europa League campaign on July 25, following Manchester City’s FA Cup final win over Watford.
Had the Hornets won, United would have been forced to cancel a game with Tottenham in the International Champions Cup in China and enter the Europa League at the second qualifying round instead.