Carvalhal - who has made a successful start to his Swansea City tenure - was eventually replaced by Dutchman Jos Luhukay, on whom the jury is still out in the eyes of several Owls fans.
And while Luhukay has succeeded in keeping Wednesday afloat this season, Palmer told Proper Sport Dyche would have taken them up.
"I’ve got to be honest with you - sorry Burnley fans - I was touting him for when Carlos left I wanted Sheffield Wednesday to break the bank to go and get him," said the former Owls midfielder - who claims to have been talking up the Burnley boss for 'three or four years'.
"I’m a big admirer of him. He’s done a fantastic job at Burnley. I like his approach to the game, he doesn’t believe in rotating the players if they’ve got cup games or whatever. He gets his squad fit, they can compete physically, they can compete technically.
"Sheffield Wednesday would have had to break the bank to get him, but I guarantee you if they’d done it they would have been in the Premier League next season. They’re spending big money for salaries for players, but not matching that with the quality of manager they are bringing into the football club."
Dyche is on course to lead Burnley into Europe this season, having twice led the Clarets into the Premier League.
And luring him to Hillsborough in January would have been a near impossible task, especially with interest from the likes of Everton in the league above.
Last week, Palmer told the same radio station that he is undecided about Luhukay and would be open to the appointment of either Nigel Pearson or Mick McCarthy this summer.
Can Luhukay get Wednesday firing again next season?