Solskjaer’s side now find themselves eight points adrift of the top four and just six above the bottom three, a margin which could be even narrower this time next week.
United are next in action on Wednesday, when Jose Mourinho returns to Old Trafford with his in-formTottenhamteam.
According toThe Sun, Solskjaer has told his squad that he could be dismissed if United lose both matches against their fellow big-six rivals.
The Norwegian conveyed the message to his players following Sunday’s draw with Villa, and will now hope for a reaction against Spurs in midweek.
The pressure on the former United striker has only intensified since Tottenham sacked Mauricio Pochettino last month.
The Argentinian was initially the favourite to succeed Mourinho at Old Trafford last December, only for Solskjaer to be handed the managerial reins on a full-time basis after an impressive spell as caretaker boss.
Ed Woodward, United’s executive vice-chairman, publicly backed Solskjaer earlier this season, but he could feel compelled to pull the trigger if United tumble further down the table in the coming days.
After Saturday’s derby with City, United will host AZ Alkmaar in the Europa League andEvertonin the Premier League.