The Italian joked he hoped that would not mean a return to Stamford Bridge for a third spell.
Mourinho was axed by the United board on Tuesday morning after leading them to their worst start to a league season in 28 years.
However, Sarri thinks people have short memories and says the Portuguese deserves respect because of his past glories.
And he expects to see him back in the dugout soon but insists his job at Stamford Bridge is off limits.
Maurizio Sarri has offered his support to the sacked Jose Mourinho:
👍 – 'Mourinho has a great future without @ManUtd'
🔜 – 'I'd like to see him on the bench ASAP.'
🏴 – 'Maybe in England.'
❌ – 'Not here @ChelseaFC!' 🤣
Read full story: https://t.co/t663HUrodP pic.twitter.com/ZltTi8RVZG
— Sky Sports News (@SkySportsNews) December 21, 2018
Asked if he would miss Mourinho, Sarri replied: “I think so.
“As you know very well, Mourinho won everything. He won everywhere so I like him very much as a coach and as a man.
“But I think he is right when he said that Manchester has a future without Mourinho. But also Mourinho has a great future without Manchester.
“I like him very much and I’d like to see him on a bench as soon as possible.
“Maybe in England – but not here!”
Sarri was also asked about Ole Gunnar Solskjaer after he came in at Old Trafford to take over from Mourinho until the end of the season.
“I remember him as a player,” he added ”He was a very good player. But I don’t know him as a coach.
“Of course, the job will be difficult, but I don’t know him well as a coach so I don’t know.”
Sarri’s Chelsea could now be in a direct battle with United for a place in the top four in the Premier League.
After an excellent start to the campaign, the Blues have hit a bit of a rough patch and face a huge task if they want to be genuine title contenders.
And he insists the title is a two-horse race between current leaders Liverpool and second-placed Manchester City.
“I’ve never seen Chelsea like a contender for the title,” Sarri.
“I always said that at the moment there are two teams a step ahead of us.”