The former Tottenham manager has been heavily linked with a move to Old Trafford since Solskjaer was sacked last weekend.
It is understood Pochettino was at the top of United's shortlist of possible replacements and that the Argentine is keen to return to the Premier League, however, latest reports claim the Red Devils' initial approach has been blocked by his current club, Paris Saint-Germain.
It's unclear, therefore, whether Man United can succeed with an immediate move for Pochettino or if they'll be forced to wait until the summer to bring him to Old Trafford.
Agbonlahor has backed the possible appointment, claiming Pochettino has what Solskjaer lacked, but insists that doesn't mean he will end the club's trophy drought.
"What I felt about Ole Gunnar Solskjaer, and I said it from day one, is that he hasn't got that swagger about him," former Aston Villa captain Agbonlahor told the talkSPORT Breakfast.
"You look at Steven Gerrard, you look at [Jurgen] Klopp, Pep [Guardiola] - they've got that aura about them to go into a changing room and demand things.
"I could imagine Ole Gunnar Solskjaer losing a game and saying, 'You know what, take tomorrow off, we'll get back in Monday, we'll try again'.
"These big managers will go in there and demand more, demand more at half-time, demand more on the pitch.
"They have the passion that shows they're actually engaged with the team.
"This is what I think maybe Pochettino will have when he comes into Manchester United.
"They'll be big pressure for him when he does come in because if they don't finish in the top four when he comes into the club, that's a dreadful season for Manchester United.
"They're a million miles away from Chelsea, a million miles away from Liverpool, more than a million miles away from Manchester City.
"They're not going to win the Premier League. I can't see them winning the Premier League for a long time.
"It doesn't matter about going and buying the best players - they haven't got a way of playing.
"You watch Manchester United and you ask, 'How are they playing?'
"There's no system. You don't see the full-backs of Manchester United coming inside and making runs.
"So, it's a tough job for Pochettino or for anyone that comes into Manchester United because the expectation is to win things and the only thing I can see Manchester United winning is maybe an FA Cup, if they're lucky."