Pochettino’s Chelsea team face Palace at Selhurst Park on Monday night, with the Eagles in poor form under Hodgson having won just twice in their last 14 matches.
Large sections of the Palace fanbase were disappointed when 76-year-old Hodgson was kept on as manager for this season, and plenty want chairman Steve Parish to replace him following the team’s difficult run.
“Nothing to say about Roy,” said Pochettino. “Roy is my friend. I admire him — he’s an unbelievable coach. I think he’s working really well. There is always pressure in football when you lose one or two games, but no doubt he is going to be successful with Palace.
“He has the experience to manage everything in this situation. It is going to be good to see him Monday. For sure, we are going to share a very nice time together.
“From the beginning when I arrived at Southampton, he was the coach of the national team and was always at Southampton watching games and sharing time with us. We made a very good relationship.
“From the first moment, the feeling was very good between us. We understand football very well, the experience is there.”
At 76, Hodgson is the Premier League’s oldest manager. Asked whether he too might still be coaching when he’s 76, Pochettino, who is 51, said: “I will only be thinking about being alive! If I am and I have the energy, I don’t know — maybe.”