Solskjaer has won seven and drawn one of his eight league games in caretaker charge to close in on a top-four finish, but United remain 14 points behind leaders City and Liverpool with 13 games left to play catch-up.
United have not won the Premier League since Ferguson retired in 2013, securing just three major trophies -– one FA Cup, one League Cup and one Europa League — in those six years.
Solskjaer, who won 12 trophies as a United player under Ferguson between 1996 and 2007, does not know if he will still be managing the club once his temporary arrangement finishes at the end of this season.
However, he is determined to ensure that, in the long term, United can become Premier League champions again, taking their victory at title contenders Tottenham in January as a sign that they are capable of doing so.
“I think we’re too far behind this year, obviously. You’ve got to catch up with the other teams ahead of us, especially Manchester City and Liverpool, but now Tottenham –- they’re really in the running as well,” said Solskjaer.
“There are three teams who have been far ahead. We’ve beaten Tottenham, so we know that we’re capable of that but we need the consistency.
“Two years’ time is long enough, but also short enough, to say that we’ve got the possibility to make a big difference in our preparation, in everything.
“Next year: you always hope, of course. When I went to Molde as manager, they were 11th in 2010, and in 2011 we won the league, so you can never say never.”
United’s immediate target in the league may be a top-four finish, but there remains the chance of silverware in the Champions League and FA Cup.
“Challenging for every trophy,” said Solskjaer when asked what United’s targets should be. “That’s what we should be about.
“We have to move slowly because we are fifth at the moment. There are six very, very good teams (in the Premier League) and all will challenge for the trophies.
“But we’ve got the resources, the infrastructure and the history to move towards the top and that is the only way we should think about things at Manchester United.”
United can move back into the top four for the first time since the opening weekend of the season with victory at Fulham on Saturday as fourth-placed Chelsea are not in action until Sunday when they make the daunting trip to the other side of Manchester to face City.
And Solskjaer is increasingly confident of securing Champions League football next season.
“I’m very confident. The players have shown me they have the character. They have the belief and they have the quality to improve,” he added.
“That’s what we have to think about: How we improve. That gives me the confidence and belief -– what I have seen at the training ground.”
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