Sancho’s Borussia Dortmund teammate Marco Reus claims the 20-year-old is not ready to leave the “peace” of Germany by heading to Old Trafford or any other suitor.
Leading figures at Dortmund believe United are in pole position to land the former Manchester City starlet – and the German giants will not stand in his way at the end of the season.
Solskjaer also believes he will have the advantage over the majority of his rivals, due to United’s spending power – even after the coronavirus pandemic.
But Reus told Sport Bild: "Jadon is an outstanding player and will definitely remain in demand by many clubs. That is a fact.
“He's now playing at an even higher level than last year and would be extremely valuable in achieving our goals.
"I would advise him to stay at BVB for another year, maybe two. From my point of view, there is no better place for him at the moment.
“Afterwards, he can take the really big step as an even more complete player, having developed further in peace here as a regular starter.
"He would have to find his place at a new club, which isn't always easy for a 20-year-old. Just how interesting do you think Jadon will be for the biggest clubs if he spends one, two or three years more here to develop further?"
Dortmund want around £120m for Sancho and insist they will not lower their asking price even though clubs around Europe are dealing with the financial fallout of Covid-19 suspending the game.
But Solskjaer is adamant United can exploit the transfer market this summer as he targets Sancho, Jack Grealish and James Maddison.
"Football is going to get back to normality at one point, and it's very important we're ready when that happens,” he told Sky Sports.
"We want to be the best at everything, and of course now is a chance to spend more time, you discuss players, discuss plans, we've evaluated what we need, of course with the coaching staff we've looked at games, evaluated games, discussing on video calls like this.
"Then, the market, who knows how the market is going to react to this? Who knows which clubs need to sell players? There might be just a situation there where you can exploit, and I know that we at Man United we are one of the biggest, and the biggest, financially well-off.
"I'm sure we are capable, when we get back to normality, that we can do the business that we want to."
Dortmund are hoping Chelsea and Liverpool will spark an auction for Sancho and are adamant he won’t be allowed to go on the cheap.
Last month CEO Hans-Joachim Watzke told Bild: "Even before the coronavirus outbreak, we said that we prefer that Jadon stays with us.
"At the end of the day, however, you always have to respect what the player wants.
"I'll say clearly that even the very rich clubs shouldn't believe that they can come here to snap up bargains.
“We don't have to sell anyone for less than they're worth."