The Red Devils have enjoyed six-game winning run under the caretaker boss, including their 1-0 win over bitter rivals Tottenham Hotspur last weekend.
Prior to his arrival, the Old Trafford outfit suffered back-to-back defeats to Valencia and Liverpool and managed to win twice in eight games across all competitions which led to the sacking of Jose Mourinho.
And the 34-year-old is backing the Norwegian tactician to continue with the impressive performance so as brighten his chances of securing the job on a permanent basis.
“When you step into management especially big job like that you just want to do well first,” Bamba said on Sky Sports.
“And obviously if you do well, you raise questions and people are going to start wandering if you can get the job permanently or not.
“But I think what you can do is what he [Ole Gunnar Solskjær] is doing now, winning games and making the team play well and I think Manchester United under Solskjær are full of confidence.
“They play with flair, they are going forward. [Paul] Pogba is now expressing himself on the pitch and that makes a difference.”
Manchester United have climbed to the sixth spot since Solskjaer took charge, tied on 41 points with fifth-placed Arsenal who have a superior goal difference.
On Saturday, they play host to Brighton & Hove Albion and will be looking to extend their winning run.