Hodgson stepped down at the end of last season after four years at the helm, bringing an end to his managerial career which stretched back to 1976.
The former Arsenal captain was appointed on a three-year deal and the club currently sit 10th in the table, with just two defeats so far this season.
When asked if Vieira had learnt from his former Gunners boss Arsene Wenger, Hodgson told the PA news agency: “I think Patrick’s learnt a lot from quite a few people along the way but there’s no doubt that he’s done a wonderful job so far at Crystal Palace.
“I’m delighted to see that and of course I’m really convinced he’s going to go on to better things with the club.
“Because the club’s in very good shape – especially in his hands – so I certainly wish him well and who knows, maybe in the future we’ll be seeing a film about Patrick Vieira’s managerial achievements.
“I would like to think so.”
:: Roy Hodgson was speaking at the world premiere of Arsene Wenger: Invincible at the Finsbury Park Picturehouse
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