United host the Reds on Sunday night at Old Trafford, in what is an important clash in the Premier League title race. The Red Devils are currently sixth on the league table, while Jurgen Klopp's side are third, and Solskjer admitted his side were lucky to finish ahead of Liverpool last season.
"It's going to take everything to get results against the best teams in the world and Liverpool are one of them," said the United boss. "They're one of the teams we're chasing. What they've done in the last four years is something we're striving towards and trying to go past them.
"We ended up above them last season but they had a very bad spell, maybe because of bad luck with injuries - now they are back to their best. We have not won the league in the last eight years. You can understand Manchester City or Liverpool walking on to the pitch and thinking quality is enough. We have players who need to keep on improving and developing."
However, Solskjaer did admit that it is way too early to talk about the title race. "To be seven behind is going to be a big distance, but if we win it would be one point," he added. "It's so early in the season, every game matters just as much."
Liverpool have scored at least three goals in each of their away games this season, and Solskjaer added: "Liverpool are on a great run of form, showing some individual skills that you almost cannot defend against. As a team, we have to be compact, aggressive, with a strong mindset and physical energy."