"When you start on something you stick to that plan.
"I'm not gonna change six or eight, or nine or 10 months into the job and start believing in a different way.
"I'm gonna stick to what I've been trusted to do by the club, and hopefully that'll be good enough, that what we can see is right. All my conversations with the club have been positive."
The coach also said they "can't react to all the noise outside" and that he, the club and staff "are very strong mentally and we're sticking to what we believe in and I've got full faith in what we're doing."
Solskjaer was permanently appointed as United boss in March last year. Since then, the team have won just 11 of 32 Premier League matches and lost 12 times.
However, he believes supporters recognise the job he has on his hands:
Simon Stone @sistoney67
OGS: "Our fans know what we have started on. I've been trusted to do job by club. Doesn’t go one way all the time. Foundation has to be laid. Culture has to be set. You don’t start with the roof. We have had a couple of rainy days and we wish the roof was on but we can’t hide."
The Norwegian expects the rebuild at United to be a lengthy process, too:
On the January transfer window, he added: "We're still working on one or two things so let's see if the club get it over the line."
United have been heavily linked with a move for Sporting Lisbon star Bruno Fernandes this month. The Red Devils have been in desperate need for creativity in their side, and with Marcus Rashford now injured for the coming months, they could use more goals, too.
Fernandes can offer both. In 27 matches for Sporting this season, he has contributed 15 goals and 14 assists.
However, the two sides' failure to agree a fee for him has reportedly caused the deal to stall, per Simon Stone of BBC Sport.
In the meantime, the Red Devils could be boosted by the return of Victor Lindelof and Eric Bailly for the Tranmere clash.
Solskjaer said Lindelof has recovered after an illness and could feature at Prenton Park, while Bailly has played "a couple of behind-closed-doors games," and there are no fresh injuries to deal with.
United could face a tricky test against Tranmere, who knocked out Watford in Thursday's postponed third-round replay, particularly thanks to the pitch at Prenton Park:
Solskjaer said of the pitch:
"Eric is one of the team who's more prepared for that pitch," he added.
Tranmere are 21st in League One, but United have won just five of their 17 matches away from home this season in all competitions.
Three days after the FA Cup tie, the Red Devils will then seek to overturn a 3-1 deficit at Manchester City in the second leg of their Carabao Cup semi-final.