United are pushing the top teams in the league with their present form, as they are now unbeaten in 16 games.
Having won their last four, United are now two points away from third place in the league.
And Solskjaer thinks they can go on to another level next term and beyond.
"I'm sure Manchester United will mount a challenge and get back to winning the league," Solskjaer said.
"When that's going to happen is up to every single one who's here and how quickly we can make this process go, we're developing as a team, improving and we've come a long way in one season so let's take Paul's word into the dressing room and expect and demand more every single day."