Fury, 28, is back in training but has not fought since beating Wladimir Klitschko on points in November 2015.
Fellow Briton Joshua, 27, stopped the Ukrainian last month in the 11th round of a fight that went back and forth.
Froch said Fury had "kind of played with Klitschko", while Joshua "struggled" when he fought him.
The three-time super-middleweight champion was a ringside commentator as Fury beat Klitschko in Dusseldorf to become world heavyweight champion.
Speaking on the Friday Sports Panel on BBC Radio 5 live, Froch said: "He had his hands behind his back at times.
"He was tapping his foot and was goading and was nonchalant in his mannerisms from the first bell right through to the last - and this is a guy that Anthony Joshua struggled with."
Fury is the subject of a UK Anti-Doping hearing, which relates to a failed test in June of last year, and a potential fight between him and Joshua could depend on the outcome.
Froch, 39, says Fury needs to get himself into fighting shape before he considers taking on the unified world champion.
He said: "He's been out of the ring two years, he's had issues that I don't want to bring up, so is he going to be the same guy who beat Klitschko?
"Of course he isn't. He's probably going to need a couple of fights but he's certainly a really exciting and interesting addition to the heavyweight division."
You can hear more from Froch on Fury and Joshua by downloading the Friday Sports Panel podcast. He also talks about unsuccessfully trying to "bury the hatchet" with former foe George Groves, who he beat in a blockbuster fight at Wembley Stadium in May 2014.
Tyson Fury's claim he would deal with Anthony Joshua "like a cat playing with wool" is "difficult to argue with", says former world champion Carl Froch.