The Southampton and QPR bosses believe a return to Stamford Bridge for the "fantastic" Portuguese coach would present a "welcome challenge" for his fellow top-flight managers
Goal.com revealed on Wednesday that Mourinho is expected to return to Stamford Bridge next season, with Atletico Madrid striker Radamel Falcao set to join him.
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"Facing the best managers is always a welcome challenge so I would welcome that," Pochettino told reporters. "I would like him to return to the Premier League.
"I know that he is well respected and well loved in this league. I know that he likes this league as well."
QPR boss Redknapp, meanwhile, hailed current Chelsea coach Rafael Benitez but suggested a Mourinho return is what Blues fans and players want to see most.
"I think he is a fantastic manager and brightens up the Premier League," he added.
"Rafael Benitez has done a great job at Chelsea, I went there last night and saw them and he has done himself no harm with the job he has done there.
"But it is common knowledge that the Chelsea fans want to see Mourinho back and I think the players probably would.
"He is a character and a great manager - you look at his record and it is fantastic."