A 1-0 win at Burnley on Tuesday, ground out in freezing temperatures against an awkward and physical opponent, put United three points clear at the top of the table ahead of Sunday's clash with champions Liverpool at Anfield, Reuters reported.
Sir Alex Ferguson was still in charge of the club when United was top after 17 games in 2012 and in that season, his final at the club, United went on to win the title.
Whether Solskjaer's side is capable of such an achievement is something of which many remain skeptical – and Sunday's game should give a clue as to its chances – but even being in the title race is exceeding expectations.
"It's a brilliant position to be in," said Solskjaer.
"Of course we know we’re going to the champions, they’ve had an unbelievable three-and-a-half seasons so we know that’s going to be a difficult game for us but we’re ready for it.
"I think we couldn’t have asked for a better time to play them, because we’re in good shape, in good form, we're hungry – that’s the big thing, these boys are hungry. They want to get better and that’s a test again, a test of character and a test of quality," he added.
Few, if any, pundits felt United was ready to challenge Liverpool and Manchester City at the top of the table at the beginning of the campaign and its poor start to the season led many to wonder if Solskjaer was even the right man for the job.
A home defeat to Crystal Palace on the opening day was followed by a 6-1 hammering from Tottenham Hotspur in the next home game.
A dull 0-0 draw with Chelsea at Old Trafford was followed by another poor home display in the 1-0 loss against Arsenal on November 1.
Yet since then United have accumulated 29 points from a possible 33 and with seven wins out of eight in an unbeaten campaign on the road, Solskjaer's team has finally found the consistency needed to challenge.
Strength in depth
If there is one aspect of the United team that should give its fans confidence for the second half of the season it is its strength in depth.
Last season, United struggled whenever it was forced to alternate its starting lineup but it now has plenty of options it can use without a significant drop off in quality.
Scott McTominay and Brazilian Fred have enjoyed a good spell as the defensive midfield pairing but at Burnley, Solskjaer wisely opted for the more physical presence and experience of Nemanja Matic alongside Paul Pogba.
Pogba got the winning goal and delivered another confident display, the latest indication of the Frenchman's strong spell of form, while the Serb provided the solidity to neutralize the home side.
"I've always said Paul is a big, big player for us. He’s a good character in the dressing room, he’s always one that the lads look to, he’s a world champion of course and we’re seeing the best of Paul at the moment. I feel he is getting better and better for every game," said Solskjaer.
Sunday will be the biggest test though for a side which is improving but which has yet to prove they are title material and Pogba is relishing the prospect.
"We have to keep calm, now it is the big moment. We will see what is going to happen," he said.
"It will be a beautiful game for everyone. A big game coming up so let's get ready for it."