Pochettino is now available after being sacked by Spurs on Tuesday night - and replaced by ex-United boss Jose Mourinho - but Solskjaer's future is said to be unaffected by the developments in north London.
United head to fifth-placed Sheffield United this weekend and could overtake their opponents with victory at Bramall Lane, as the club look to recover a nine-point deficit to the Premier League's top four.
A top-four Premier League finish alone would not represent a triumphant 2019-20 campaign for Manchester United, according to Marcus Rashford, who has his sights set on major trophies.
There has been talk that United could consider turning to Pochettino to take over from Solskjaer, whose side have only managed two more points than Spurs from their opening 12 Premier League games of the season.
Tottenham Hotspur's Kyle Walker-Peters, Mauricio Pochettino, Ben Davies and Danny Rose celebrate after the UEFA Champions League quarter final second leg match at the Etihad Stadium, Manchester last season on their way to the final.
United are now in seventh place in the Premier League, nine points off the Champions League places, after a mixed start to the season.
Dogs kill pregnant woman in France during hunt
The pack of hounds was hunting deer, the local newspaper Le Courrier Picard reported. The police have launched an investigation into manslaughter by dog attack.
"I think it's been 18 months since we won our last trophy so it's not long".
Ed Woodward, United's executive vice-chairman, has moved the club away from signing players in their late 20s and early 30s following disappointing investments in Bastian Schweinsteiger and Nemanja Matic in recent seasons.
"There was no hesitation from me over signing a new contract and it was the same for Ole as well", Rashford told Sky Sports News.
"I could see where he wanted the club to be".
"We were on the same page and wanted the same things for the club". Ole is a enormous man and he has the club's interests at coronary heart so there's now not a bigger particular person for the job personally'.
'Now we would like to bide our time and righteous be patient, as prolonged as we help working hard and factor in in what we're doing - which I mediate the crew attain 100 per cent - then I mediate we would be good'.