Following a poor start to the season, Manchester United were not expected to be in the title picture, but things have changed over the last two months.
They are on an unbeaten run of eleven league games, winning nine of them and are going to Anfield on Sunday as the league leaders with a three-point lead over champions Liverpool.
But Whelan feels their defeat to Manchester City in the EFL Cup semi-final showed the difference between the two sides and he believes the jury is still out on whether Solskjaer is the man to lead Manchester United to a Premier League title.
He insisted that the Norwegian has been doing a good job at Old Trafford but stressed that he does not have the squad to take on a Manchester City or a Liverpool yet at the moment.
Whelan said on LFC TV: “I think the Man City games showed a lot about what United are.
“They have been really good of late, [Brunp] Fernandes has been a great signing but the gulf between Manchester United and Man City the other day was miles.
“Man United fans are thinking will Ole be able to take them to the next level? This run has been so good, but they have to keep it up, they have to try and win the league.
“They are still unsure whether Ole Gunnar Solskjaer is the man that can lead them to it.
“I don’t think they are good enough yet and I don’t know whether they have big signings to come in until the end of the season.
“But for me, at this moment in time, he is doing a very good job.
“He cannot reach the levels of Liverpool and Manchester City because he doesn’t have the players yet.”
Manchester United are at the top of the league table in January for the first time since the 2012/13 season when they last won the league title.