Bailly has shaken off long-term injury problems to star for United in recent weeks.
Solskjaer told MUTV: "Eric speaks many languages so he's one that connects people.
“We know Eric has had a tough few seasons with injuries, and tough spells, but he always gives 100 per cent.
“He gives everything for his team-mates. He's one of those that you want in your team, you want in your side if there's a battle going on. He's just a very likeable person.
"You see the harmony and unity in the group. I believe this is going to be important this season, with the fixture congestion and the schedule, that players know they have the chance and possibility to contribute - and they will contribute throughout the season. "
“Eric has played the last four now and he's been absolutely top."