One source added that Solskjaer knew he had to win on Saturday and is now expecting the worst.
Despite humiliation at the hands of Liverpool and Manchester City, United chiefs, including co-chairman Joel Glazer and executive vice chairman Ed Woodward, were keen for Solskjaer, who signed a new three-year contract in the summer, to at least see out the season.
But the manner of the performance at Vicarage Road and United's fifth defeat in their past seven games warranted fresh discussions between Glazer and Woodward on Saturday night. Chief negotiator Matt Judge was also involved in talks.
Talks among executives late on Saturday focused on compensation costs for the manager, as well as which of his staff would stay on at Old Trafford in the event of his dismissal.
A lack of alternatives and results in the Champions League -- United are top of Group F with two games to play -- have kept Solskjaer in the job during a miserable run of results, but there are now genuine fears the Norwegian will not be able to get the team into the top four and earn a place in the financially lucrative Champions League for next season.
There are varying levels of support among United executives for Mauricio Pochettino, Brendan Rodgers, Zinedine Zidane, Erik ten Hag and Ralf Rangnick to take over, but all of the candidates except Zidane are employed at other clubs.
There would be support for technical director Darren Fletcher and assistant coach Michael Carrick to lead the team in the interim, but the duo are untested as top-level coaches and United are facing a daunting run of 10 games in five weeks before the end of the calendar year.
The latest setback against Watford has seen United slip to seventh in the table.