Murphy believes Leicester City boss, Brendan Rodgers would be a better option than Paris Saint-Germain’s Mauricio Pochettino due to the Northern Irishman’s experience of managing Liverpool.
Solskjaer was dismissed by the former Premier League champions on Sunday after he led the Red Devils to a 4-1 defeat away at Watford.
Michael Carrick has taken over now as a caretaker manager and will be in charge of Tuesday’s Champions League clash against Villarreal in Spain.
Both Pochettino and Rodgers are said to be willing to leave their current appointments immediately if United come calling.
Rodgers was in charge of Liverpool for three years before a stint at Celtic, and most recently led the Foxes to FA Cup glory last season.
And Murphy thinks Rodgers would be a better choice than Pochettino.
“It doesn’t surprise me there’s a link with Brendan and United at all,” he told talkSPORT.
“Do I think he’d take it? Yes, I do. I think I’d go with Brendan ahead of Pochettino. I think the experience of Liverpool.
“He’s been at a massive club and understands the expectations. I know Poch is at PSG and I know he was at Tottenham – it’s a big club but it’s not the same expectation being at Tottenham as it is at Liverpool and Manchester United.
“So he’s got that little bit of extra experience by managing Liverpool rather than Tottenham. They’re both tactically good.”
Murphy also feels that former Tottenham boss, Pochettino is a ‘risk’ due to the lack of silverware he has won as a manager.
“Why aren’t you [United] aiming high? Why aren’t you aiming for the best? If Pochettino is the one, fine, but why is he the one? Because the fans wanted him 18 months ago before he struggled at Tottenham?
“For me, he’s a manager who is yet to be proven at a top-level club winning things consistently. He made Tottenham into a competitive side by coaching players well, making them better collectively and individually. He did a great job at Spurs with players who wanted to be coached and get better.
“He’s going to be walking in as he is at PSG – where he’s struggled a bit, to be honest, he can’t seem to integrate the front three together.
“I like him but no [I wouldn’t go all out for Poch] because it’s a risk.
“He’s yet to show that he can deal with top-class international players over a period of time and win things.”
