Roy Hodgson’s contract with the Eagles expires at the end of the season, with no indication yet as to whether or not he will sign an extension at Selhurst Park.
If the 73-year-old does leave Palace in the coming months, it will catapult the south London side into a race to secure a new manager, with reports stating earlier in the week that they have already identified Dyche has a potential candidate should the role become vacant.
And Ambrose, who spent three years at Selhurst Park during his own playing career, has claimed that a move to the capital would be a step forwards for the 49-year-old’s career.
Speaking on talkSPORT, he said: “I’m good friends with a lot of Palace fans, having spent some time there.
"They’re the same – they want to see the team develop and play to their strengths now, but there’s a big risk behind that, of course. It could go horribly wrong and you could end up in the Championship very very fast, the way Premier League is.
"If it’s going to change, he’ll definitely leave on fantastic terms, Roy Hodgson, whether it’s this season, next season.
"For me, you’ve got to be looking, although he’s been linked with Celtic, at an Eddie Howe, potentially – I really like Sean Dyche I think he’s a fantastic manager who’s probably overachieved with the players he’s had at Burnley over the seasons.
"A manager's going to have to come in knowing that they have to reshape the whole club, so you need someone who has enough experience and enough nous about them that can come and do that, and I think Sean Dyche could be that man.”
When asked if switching Turf Moor for Selhurst Park would be step up, Ambrose added: “I think with the squad they [Palace] have got, yeah.
"I think when he joined Burnley, he’s overachieved with the squad they have.
"Burnley are a good club, they’re a regular Premier League club, but in my opinion, it is a little step up.”