Liverpool are tied with Manchester City at the top of the current standings and can take an outright lead if they win or draw at Old Trafford on Sunday.
Solskjaer said the 29-year wait for the trophy will be at the back of their opponent's minds.
"Of course they do feel that pressure. I think all the supporters do and players probably do as well," Solskjaer told reporters ahead of Sunday's clash.
"But then we have not won it for a few years and so we want to get back to that. We have to make sure that we don't end up being happy being among the top four.
"If you aim too low and reach your target, then that's more dangerous than aiming too high and missing them. It's probably the toughest league to win and when you look at it, there are only five or six teams that have won the Premier League."
Solskjaer also took a dig at Liverpool, who have shown potential to be title challengers in recent years before fading away and relinquishing their advantage in the title race.
"I have loads of Liverpool fans back home and every year is going to be their year. It has got to October and it's: 'OK, next year'," Solskjaer added.
"Now they are in the race so for them, it is going to be an exciting finish to the league. That's none of our concern, we just have to concentrate on ourselves."
(Reporting by Rohith Nair in Bengaluru; editing by Sudipto Ganguly)
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