The 45-year-old has made a record-breaking start in charge at Old Trafford, becoming the first boss to begin his United career with eight straight victories.
That has led to a growing clamour from supporters for Solskjaer to be confirmed as manager on a permanent basis, despite United still being linked strongly with Tottenham's Mauricio Pochettino.
Victory away at Pochettino's Spurs and Arsenal in the FA Cup on Friday have dismissed suggestions early in Solskjaer's run that he had just benefitted from a kind run of fixtures.
"I love it," said Solskjaer ahead of Burnley's visit to Old Trafford on Tuesday. "It's what you want, we've had some fantastic results, great performances.
"And the improvement I can see in many aspects, just from Tottenham to Arsenal; the way we improved the structure, the ideas, we've got to know each other more and they've got to know me and what I want from the team.
"For a few games everyone said it was just about attacking, attacking, attacking but it's the other part I've been happy with. We've not conceded many chances."
Solskjaer was appointed till the end of the season after Jose Mourinho's sacking last month to buy the United hierarchy time to find a permanent replacement with Pochettino widely rumoured to be their prime target.
However, Solskjaer's case is becoming hard to ignore and he is already looking to the future by hoping to give a number of the club's most promising youngsters games before the end of the campaign.
"We have quite a few talents in that youth team that you'd like to see," said Solskjaer.
"And will see at some point before next season, to put the club and team in a good position at the end of the season, how will we look next season.
"Mason (Greenwood), Jimmy Garner, Ethan (Hamilton) - it's just about the right time.
"We've got Alexis (Sanchez), Romelu Lukaku and Juan (Mata) who haven't played so much lately. They're three players they have to jump ahead of.
"What Manchester United are going to look like next season with or without me, it doesn't really matter. I'm here as part of that to prepare the team for next season. That means doing well now."
Solskjaer's wish to blood youngsters may be tempered by United's charge towards the top four.
Victory over the struggling Clarets at Old Trafford could move the Red Devils into the Champions League places for the first time since the opening weekend of the season.
However, United have not added to their squad to bolster their challenge on three fronts in the January transfer window and Solskjaer is therefore keen not to lose any players despite suggestions defender Matteo Darmian could return to Italy and that Brazilian midfielder Andreas Pereira could go out on loan.
"At the moment I can see everyone staying at the club. No deals have been done with anyone," added Solskjaer.
"It'll be good to get the window closed and concentrate on improving the players in the squad still here.
"I can't see Andreas going out on loan because he has done fantastic in training ever since I come back, and he's a player I can see playing quite a few games for us towards the end of the season."
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