"I think I earned myself a title shot at that belt and thats what I'm, petitioning for.
"I'm 100 per cent ready....I deserve that shot."
Whittaker, 26, has won seven straight and hasn't lost in more than three years.
The middleweight title is presently the property of Englishman Bisping, whose next defence will be against former welterweight champion Georges St-Pierre, though no date has been set.
Speaking on his podcast, Bisping said Whittaker should be his next challenger after St-Pierre as he would be a more worthy contender than No.1 ranked Yoel Romero, who wasn't able to stop Souza.
"Robert Whittaker looked great, the kid is on fire," Bisping said.
"I've nothing but praise for Robert Whittaker, good footwork, decent takedown defence. "He's had seven wins in a row and he's doing good, he's knocking out some people as well and he looked great against Jacare.
"He called me out on the microphone immediately after and of course he should do that. "Fair play to to him and I've got no qualms about fighting Robert Whittaker."
No.2 ranked middleweight Luke Rockhold is reportedly also impressed with Whittaker's performance last weekend and interested in scheduling a fight.
- AAP