Solskjaer, who was a forward at United for 11 years, had also earned praise from Liverpool manager Juergen Klopp last week, who said the Norwegian "deserves (the job) 100 percent".
"I think they will," Hasenhuttl told reporters on Friday when asked whether United would give Solskjaer the United job on a permanent basis.
"To be unbeaten (in the league) since he took the job is amazing, it's outrageous.
"With his history of being a player at Manchester United and now doing it as a manager in a very good way, I think you can't have better science to be the next manager."
Southampton, in 17th place, are just two points above the relegation zone with 27 points but Hasenhuttl said their midweek win over Fulham had eased the pressure on his squad before Saturday's trip to Old Trafford.
"I'm positive, we had a very important win on Wednesday and now we go with not much pressure, because nobody expects something from us," Hasenhuttl, who took over at Southampton in December, added.
"It is very hard to take points at Old Trafford but my team does not think in that way.
"We know we can be a good opponent in every stadium for every team, if we are very organised, as we showed against Chelsea (in the 0-0 draw) for example, where it is not easy to take a point."
(Reporting by Rohith Nair in Bengaluru; Editing by Keith Weir)
