The Red Devils turned to the former striker to take over the reins from Jose Mourinho back in December following a 3-1 loss to Liverpool FC at Anfield.
Solskjaer made an immediate impact at the Old Trafford side and managed to go on a long unbeaten run in domestic competitions.
Manchester United managed to overturn a 2-0 deficit to beat Paris Saint-Germain 3-1 in the second leg of their last-16 tie to reach the Champions League quarter-finals.
The Norwegian coach has experienced his first setback as Manchester United manager after the Red Devils lost successive games to Arsenal and Wolverhampton Wanderers.
Pochettino has been regularly linked with the Red Devils role over the past two or three season during the low points in Mourinho’s reign.
Former Chelsea FC defender Burley believes Pochettino would be a better appointment than Solskjaer.
“If it wasn’t Manchester United and there was another club to be managed, and there was a choice between Solskjaer and Pochettino, it’s not even close – it’s Pochettino,” Burley told ESPN FC.
“So why should it be different because it’s his former club?
“Over a short period at the moment he’s done a great job, but who would you prefer to try and peg back Klopp and Guardiola with a big budget?”
Manchester United will return to Premier League action with a home clash against Watford on Saturday 30 March.
The Red Devils will take on La Liga champions FC Barcelona in the Champions League quarter-finals next month.
Manchester United are in fifth place in the Premier League table and two points behind Arsenal, who occupy the final Champions League spot.
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