Pogba sustained the injury during the 2-0 win over Newcastle at St James' Park after a challenge on him by Jonjo Shelvey which ruled him out of the FA Cup third round win over Reading last weekend.
The first-team squad flew out to Dubai for some warm weather training this week and the France midfielder joined the group later in the camp. Having been assessed, Pogba is expected to start the game on Sunday at Wembley.
"He looked OK towards the end, and I think he'll be fit. He had a problem, but he's come through the last few training sessions and I think he'll be OK to play," Solskjaer said.
Manchester United's French midfielder Paul Pogba (C) shows his leg to Newcastle United's English midfielder Jonjo Shelvey (2l) following a cahllenge from Newcastle United's Enlish midfielder Isaac Hayden (L) during the English Premier League football matc
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"We had four good days of training, so I think the boys enjoyed it. We laid a few principles down, we worked hard and I think they enjoyed it."
Meanwhile, defender Marcos Rojo has returned to Argentina to receive treatment with no return date set.
Solskjaer will come up against Mauricio Pochettino in what has been billed as an audition for the United post on a full-time basis.
When asked to rate the job Pochettino has done at Spurs, Solskjaer added: "He's done a very good job. Speculation is there for a reason because he's done well. It's not my job to rate all the different managers, it's my job to focus on my team."
Ole Gunnar Solskjaer is making a strong case to be given the Manchester United manager's job full-time
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The trip to face Tottenham comes off the back of an immaculate start to Solskjaer's tenure as caretaker, but the Sunday clash has been viewed as the first real test since he replaced Jose Mourinho last month.
But the Norwegian said: "No, we've had tests. Newcastle away was also a test. Cardiff away was also a test, you get tested every single game in the Premier League.
"But this is against a top side. If we want to get closer to them and go past them, we need a big performance and a big result."
Harry Kane's penalty reignited controversy about VAR (Nick Potts/PA)
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Harry Kane has scored eight goals in his last eight Premier League starts and Solskjaer admits it will be tough to keep the England captain quiet this weekend.
"He’s not bad is he? He is a fantastic goal scorer and one of the best in the world, but I have got a couple that I’m happy to work with.
"He is a top professional. Sure, whoever plays with him and trains with him can talk more about him, but from the outside he is a fantastic finisher. He never misses chances so let’s make sure he doesn’t get any against us."