De Gea was substituted during Spain's draw with Sweden on Tuesday due to an abductor problem, while Pogba has missed United's last five games with an ankle injury.
"David needs a scan," Solskjaer told Sky Sports of his Spanish goalkeeper. "I think he'll be out. It certainly looked like it anyway judging on last night so it's just one of those things.
On Pogba, Solskjaer added: "Paul had an injury, he came back, he worked really hard. He came back and played a couple of games, maybe played through the pain barrier.
"He had a scan after the Arsenal game and maybe needed a few weeks' rest in a boot so hopefully he won't be too long, but he won't make this game, no."