The English top-flight will be back in action in two weeks after several months of coronavirus-enforced inactivity.
United are set to resume the season away to Tottenham Hotspur on June 19 -- their first match since beating LASK 5-0 in the Europa League on March 12.
That victory in Austria extended United's unbeaten run to 11 matches and Solskjaer is in no doubt as to what his side must do to be ready as they continue their quest for a place in next season's Champions League.
"The first game is two weeks from today so we need to step up the training and get an edge to our game again," Solskjaer told United's website on Friday.
"Everyone knows that we will have to be at our best, have to be focused (against Tottenham).
"We know it's a big game for everyone. We had Chelsea when we started the league this season so I'm confident that our players can go into the Tottenham game with that mentality of going there to play a very good game of football."
Following the Spurs match, United face fellow European hopefuls Sheffield United at Old Trafford on June 24 before travelling to Brighton on June 30 -- after an FA Cup quarter-final at Norwich on June 27.
Former United striker Solsjkaer said, however, his squad had been preparing for a congested fixture schedule.
"Training has been about recapping what we did well, tweaking maybe one or two things and looking at some new ideas, but hopefully we can see a lot of what we saw towards the end before the lockdown.
"We've got games coming weekend, midweek, weekend for a spell so you have to focus on ourselves and not just on that one, first game," added the Norwegian, with United three points adrift of the top four when Covid-19 saw the season suspended.
"Gradually now, as we've got into contact training, you can see a little bit more of the edge but also the camaraderie and team bonding.
"That's vital for me in a team. That's one of the main things, that we are a team and the team goes before anything else."
Kane hopes Spurs can be single-minded
Harry Kane hopes Tottenham can benefit from focusing solely on the Premier League when the battle for a place in next season's Champions League resumes.
The English top-flight is set to restart on June 17, with Jose Mourinho's Spurs hosting his former club Manchester United two days later.
Tottenham have nine games to try and force their way into the Champions League places.
Mourinho's men are seven points off the top four, but fifth could be enough if Manchester City's appeal against a two-season European ban is rejected.
Win their first game back and Spurs would be just a point behind fifth-placed United.
All of Tottenham's rivals also have other things to play for with Manchester United in the FA Cup and Europa League, Chelsea in the FA Cup and Champions League, Wolves in the Europa League and Sheffield United in the FA Cup.
"From our point of view we are not in any of the other competitions so we have got nine games to concentrate on picking up as many points and try and get into the Champions League spots," Kane told Sky Sports News.
"So at least all our focus is going to be on one competition."
Kane will be fit to resume following nearly six months off with a serious hamstring injury.
He added: "It feels like a pre-season, it has been good so far. I was doing individual training for a while and almost got to a stage where I was back with the team and then we had to stay at home.
"It's been a chance for me to get fit. It has been six months since I have played a game so I haven't done that since I was about five years old."
Spurs stepped up preparations for the restart by staging an 11 v 11 training match at the Tottenham Hotspur stadium on Friday.
Earlier this week, the North London club confirmed that one individual had tested positive for coronavirus, but did not say if it was a player or member of staff.
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