The original game on May 2 was postponed after fans demonstrating against the owners, the Glazer family, entered Old Trafford and surrounded the team hotel.
Sources have told ESPN that further protests are planned when Liverpool visit Old Trafford on Thursday but Solskjaer said his players want the chance to beat Jurgen Klopp's side.
"Security measures are being looked at and I hope we can keep the protests, if there are protests, keep them down to loud voices and nothing violent," Solskjaer said.
"We want to listen, the players want to play the game, we're playing Liverpool and of course we want to beat Liverpool and we want to beat Leicester so we're going to do everything we can for our fans to celebrate what we're doing on the pitch."
Greater Manchester Police said at least 12 officers were injured during the protests on May 2.
Security has been increased around Old Trafford ahead of games against Leicester City and Liverpool this week with barricades erected across the forecourt in front of the East Stand. Police presence at the stadium is also set to be significantly increased.
Sources have also told ESPN the club have also reviewed travel arrangements for the players ahead of the games, including using decoy buses to make sure they can be transported to the stadium safely and on time.