Despite being humiliated by both Manchester City and Liverpool, United chiefs, including co-chairman and executive vice chairman Ed Woodward, were keen for Solskjaer, who signed a new three-year contract in the summer.
The manner of the performance at Vicarage Road and United's fifth defeat in their past seven games prompted fresh discussions between the two. Matt Judge was involved in the talks.
The costs of compensation for the manager and his staff were the focus of talks among executives late on Saturday.
Solskjaer has kept his job despite a poor run of results, but there are now genuine fears that he will not be able to get the team into the top four and earn a place in the top four.
The opportunity to speak to Antonio Conte was passed up by United after the defeat to the Reds at Old Trafford.
There are differing levels of support among United executives for the candidates to take over, but all of the candidates are employed at other clubs.
The technical director and assistant coach would get the support of the team in the interim, but they are inexperienced and United are facing a daunting run of 10 games before the end of the year.
The next two weeks are between the trips to Old United and the game against Newcastle United.
The latest loss has seen United slip to seventh in the table.
They play a game in Spain against Villarreal on Tuesday, then travel to London to play a game against the Blues on Sunday.
