The pair face off this weekend with the Reds closing on a first Premier League crown, having dropped just two points this term.
The only blot on their copybook in the league came, of course, at Old Trafford earlier this season, Adam Lallana scoring late to claim a 1-1 draw after Marcus Rashford had opened the scoring.
Now United head to Merseyside on Sunday, looking to give their own top four hopes a shot in the arm by again denying Jurgen Klopp’s men victory once more.
And as his United stars pitched up at Carrington on Friday morning to continue preparations, Solskjaer insisted that, despite it already being seven years since the Red Devils’ last title win, he is sure that they won’t have to wait in excess of two decades more to get back on top.
“That’s what we’re working hard to make sure doesn’t happen,” Solskjaer stated.
“And let that be a lesson for us that we can’t let ourselves go another 24 years until we win the league and I’m sure we won’t.
“I believe in this club, I believe that we are rebuilding now, we’ve started something that’s going to take a little bit of time but we’ll get there.”
Amid detailing his pessimism over Marcus Rashford’s chances of featuring on Sunday due to a back problem and naming Harry Maguire as the club’s new permanent captain, Solskjaer used his Friday press conference to heap praise on Brandon Williams.
The Norwegian was asked about the 19 year-old’s discipline, having been booked six times this term already, while becoming involved in an off-the-ball dispute with Pedro Neto during the midweek FA Cup replay win over Wolves.
But Solskjaer, set to start Williams up against Mohamed Salah this weekend at Anfield, responded: “Does it look like I need to speak to him? I don’t think so.
“I think he’s been absolutely outstanding since he came in, every challenge we’ve put in front of him he’s tackled head on.
“He’s only 19, made 10 or 11 starts but he reminds me so much of the mentality of Gary Neville and I think he’ll enjoy going to Anfield, to put it that way.”
Williams’ emergence has seen him usurp Luke Shaw at left-back, with the England international now facing a fight to reclaim his starting spot when he returns from a tight hamstring.
And that is a battle in which Shaw will hope to have far more success than Phil Jones, who continues to fall down the pecking order at Old Trafford.
Jones started in the game against Manchester City in the Carabao Cup, but endured a nightmare in the 3-1 semi-final first leg loss.
He hasn’t played since and United now have Eric Bailly back available, having missed the season so far through injury.
The Ivorian could be set for a place in the squad this weekend.