Unbeaten Groves, who faces Jamaican Glencoffe Johnson on Saturday, also said he would like to challenge for Arthur Abraham's WBO belt.
The Briton pulled out of a challenge for that title, which was then held by German Robert Stieglitz, in April.
"Having missed out on a world title shot this year when I had to pull out of the Stieglitz fight, it's logical I want my chance as soon as possible," Groves told World Boxing News. "I'm ready now, without a doubt.
"Personally, I'd love a crack at Carl. He's been such a great champion and I've so much respect for him. But he's said he only wants a few more fights and I'd love to be one of them. That would be a huge fight for Britain. I'd fight Arthur Abraham anywhere, any day of the week."
However Groves, 24, says he is not yet ready to take on WBC and WBA champion Andre Ward.
"Andre Ward is the elite of the division, the best by some way. Ideally, I'd prefer a few more before facing him. No one's even got close. I'd like to be the first to really trouble him in about a year's time," he added.
Veteran Johnson, 43, arrives at London's ExCel Arena with a 51(35)-17-2 record.
Groves is confident of getting close enough to hurt him.
"Tests show that I'm fitter which enables me to throw more shots per round, whilst still picking them correctly and throwing them with spite and venom," he said.
"I've also become bigger and stronger and, as a consequence, I'm hitting harder. Some sparring partners that I've used for quite a while are now unable to last the rounds with me that once they could.
"Finally, my defensive moves have improved. I'm definitely more comfortable in the pocket which is important because I'll need to get close to Glencoffe Johnson."