United have won four games from four in the Premier League since Solskjaer was put in temporary charge until the end of the season, but they were dealt a blow as Pogba missed their FA Cup victory over Reading through injury following an incident involving Newcastle United's Jonjo Shelvey last week.
With Solskjaer taking his side to Wembley for a tricky encounter against Spurs following a favourable initial fixture list, the United boss will be pleased to have Pogba available again, having featured in recent training sessions during the clubs mid-season trip to Dubai.
"[Pogba] looked OK towards the end so he'll be fit," Solskjaer told a pre-match news conference. "He did have some problem but he came through the last couple of sessions well. He'll be OK."
The prospect of a meeting with third-placed Tottenham should test Solskjaer's burgeoning Old Trafford credentials, but he insisted that United have not had it easy since his arrival.
"We've had tests," he said. "Newcastle away is a test, the first game at Cardiff is a test, the first home game is a test.
"You get tested in every single game in the Premier League. But, of course, Sunday's game is against a top, top side. If we want to get closer to [Tottenham], we need a good performance and a good result."
Despite the improved level of the opposition, though, Solskjaer will encourage United to attack Tottenham as they have amid their four-game winning streak in the Premier League.
"You always adapt to any opposition and we're playing one of the best teams in the league, so of course we've got to be aware of their strengths," he added.
"But I've been brought up in a way that we need to attack teams. That's our strength as well: going forward and attacking teams.
"We're not going to get as many chances to attack as we have before, so we've got to be ready for when we get hold of the ball, to play well with it and make sure we use the whole pitch as well."