Last year, after Joshua knocked out Dominic Breazeale in London, Takam followed the Brit to his hotel and demanded that he fight him.
Joshua, who has recorded 19 consecutive knockouts with only three opponents surviving beyond the third round also admitted that he got knocked down in round six during his bout with Wladimir Klitschko in April because he was exhausted.
Joshua's fight with Kubrat Pulev was cancelled this week after the Bulgarian suffered an injury in training - with Carlos Takam stepping in as a replacement.
Fury recently outlined his intention to fight three times next year but has distanced himself from the British Boxing Board of Control, which could hinder any hopes to stage a fight with Joshua on United Kingdom soil if unresolved.
Joshua's explosive power and brutal knockouts have earned the heavyweight champion hordes of fans, but the Briton insists that style will not work against every opponent.
"In terms of style of opponent, he's definitely harder to knock out", Joshua told reporters at the English Institute of Sport in Sheffield, where he trains.
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That saw him add the WBA title to the IBF belt he won in 2016.
It has been suggested that the late change of opponent may disrupt Joshua's preparation for the bout, especially with fight night closing in.
He added Takam - with 35 wins from 39 fights - was not to be underestimated.
"I would have had way too long out of the ring and I need to keep myself active, pick up on what I've learnt from the Klitschko fight, and Takam is a good title defence". I swear. It was the Breazeale fight.
An inconvenient late switch of opponent will provide a much different test for Joshua, who had been preparing to face another boxer in the Klitschko mould. I know he's game, he said he wanted to fight me as well so that's someone who believes they can beat me. He came to the fight, then waited for me in reception. I knew who he was. Speaking to Sky Sports, he admitted that it's Takam's chance to "shock the world" and that it'll be no easy task. Takam weighs 22 stone. "He was moving his way up the IVF rankings, so I've always had my eye on him anyway".