Solskjaer, appointed as interim boss last month to replace the sacked Jose Mourinho, has made clear that he would love to stay at Old Trafford beyond the end of this season, when his temporary arrangement is set to expire.
The former United striker, on a managerial loan from Norwegian club Molde, has not spoken to executive vice-chairman Ed Woodward about a longer stay.
However, he feels that the key to being seen as a success is to return to the attractive, attacking football that the club played for much of Alex Ferguson's near 27-year reign as manager.
Ferguson won 38 trophies before retiring in 2013 but his United team were also renowned for their positive football, which many fans felt went missing in the final year of Mourinho's reign.
Solskjaer, when asked what would constitute success and improve his chances of getting the job permanently, said: "If we get to the summer and people are talking about the way Manchester United are playing. If the style we're playing, it reminds us of Sir Alex's team, if it reminds us of the successful times."
Solskjaer said he is keen to win trophies this season but suggested that the style, for now, was more important.
"It has to start with the way we play because results you cannot control," he said. "You can control how you approach the game and how you play. And of course, it's about trophies — if you can get to the final of the FA Cup and get a trophy. Let's see in May if it's a success or not."
Solskjaer has won his first four matches at the helm, including a 2-0 victory at Newcastle on Wednesday, and hopes to extend that run when Championship strugglers Reading visit Old Trafford in the FA Cup on Saturday.
However, he expects there to be setbacks as he attempts to improve United's Premier League position from sixth over the second half of the season.
"When you win games of football, you're happy," he said. "There will be tougher times coming, there will be tougher games coming up, we know that.
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