According to The Daily Mail, Murphy said that it is good for the game that Manchester United are once again back in a title race in the Premier League.
Since Sir Alex Ferguson retired in 2013, United have only finished in the top two once, and have never really been involved in a title race since then.
The arrival of Ole Gunnar Solskjaer, and more importantly Bruno Fernandes, has turned United around in the last year or so. They finished third in the Premier League last season and are second in the table right now, behind Liverpool only on goal difference.
Murphy was full of praise for the job that Solskjaer has done at Manchester United since taking over from Jose Mourinho in December 2018.
"My natural instinct isn't to wish Manchester United well but I have to appreciate that seeing them in the title mix, currently joint-top with Liverpool, is good for the game," Murphy told The Daily Mail.
"The rivalry between Liverpool and Manchester City has been enthralling in recent years but nothing can compare with seeing the biggest two clubs in the country - Liverpool and United - going toe to toe."
"United's revival under Ole Gunnar Solskjaer is an example that patience can be the best policy towards a manager. There have been many times when Solskjaer has been written off or needed a result to secure his job and he's always found a way.
"That is a credit to him and perhaps a lesson to trigger-happy chairmen that you sometimes have to give managers a proper chance, particularly when they are trying to instigate long-term change."
Danny Murphy says Liverpool and Manchester City are still stronger than Manchester United
The former Liverpool midfielder, even though effusive in his praise for Solskjaer, said that he doesn't think Manchester United would eventually win the title.
Having said that, Murphy also stated that he wouldn't be unhappy to see Solskjaer win the league with United. Murphy believes that the Norwegian has a similar personality to Jurgen Klopp.
"I think Solskjaer has conducted himself remarkably well over the past couple of years," Murphy said.
"He is hard to dislike. I think they will fall just short this season, over 38 games Liverpool and City are still stronger, but he's made United competitive again.
"If the worst happens and United end up champions, Solskjaer is the one person you wouldn't mind winning because he would remain humble and take it the right way, as Jurgen Klopp did at Liverpool. If Jose Mourinho had won the league with United, it would have been something different!
Liverpool and Manchester United take on each other in a big Premier League clash at Anfield on January 17.Published 04 Jan 2021, 15:07 IST