The France international picked up what Solskjaer described as "a knock" in the 2-0 Premier League win over Newcastle United on Wednesday, in which he was caught by a high challenge from Jonjo Shelvey.
Pogba could sit out Reading's visit to Old Trafford on Saturday, while Chris Smalling and Marcos Rojo are definitely sidelined, but Solskjaer plans to play Lukaku and Sanchez as he tries to rotate his squad.
"Rojo, Smalling - they're out," he told a news conference on Friday. "I'm not sure if Paul's going to be ready; he got a knock against Newcastle. Hopefully, [Marouane] Fellaini will get through the training session today and we'll be more or less a full squad.
"There'll be a few changes and they get a chance. Some of them are itching to play. [We will] get Lukaku a start, get Sanchez a start. That's important for them because they need more game time."
United are expected to earn a comfortable win against a Reading side who sit 23rd in the Championship, and Solskjaer admits there is a level of expectation for the Red Devils to reach at least the final, as they did when they lost 1-0 to Chelsea at Wembley last season.
"Whatever competition you're in, you want to win when you're at a club like this," he said. "I'm not sure if you expect to win it but it's more or less what you do expect from a club like this and the players we've got."
After the match, United head to Dubai for a warm-weather training camp before they face Tottenham at Wembley in the Premier League on January 13.
Solskjaer thinks the break will be a good opportunity for players to build up fitness after a hectic playing schedule since he took charge last month.
"I've got to know them because I've had plenty of time to speak with them, but we haven't had plenty of time to train. It'll be a time to get some fitness work in and work hard with them," he said.
"If any of the players think it's a holiday, they're wrong! We're there to stick together, work on the physical part of it, and of course think a little bit ahead to the Tottenham game.
"They've not scared me yet! I really enjoy working with them. They want to learn, they want to improve and that's key for any footballer: if you're hungry enough and humble enough to know you've got something to improve and to work on, then we'll improve as a team in the end."