United go into Tuesday night's Premier League clash against Brighton in sixth place in the table but on a 14-match unbeaten streak in all competitions.
And with a remaining run-in of six league matches containing four against bottom six sides keeping their run going would give them every chance of grabbing that top-four spot and with it Champions League qualification
“Any Man United team should go into any game against any opposition believing they can win that game so the short answer to whether we can go unbeaten is yes," said Solskjaer.
“The long answer is that there's more to it than that but we hope to extend it and want it to go on as long as possible.
“Of course we are delighted with the way things are going at the moment but we are just going to take one game at a time."