by Simon Crawford
Groves defeated his fellow Londoner and reigning IBF world super-middleweight champion in the amateurs back in 2006 and again in the professional ranks when he edged a points decision in 2011.
With the 'Saint' finally becoming a world champion at the weekend at the fourth time of asking, it appears as though the duo are on collision course once again.
"It should be an easy fight to make but he is not an easy person to deal with," Groves told sportinglife.com.
"I would certainly like it to happen. I've beaten him twice already and it's a fight everyone would like to see.
"I'm not sure what his situation with the IBF is - I think he may have a mandatory defence against Andre Dirrell first, but if that can be sorted we can make what will be a very big fight and I'll enjoy beating him again.
"Now I'm a world champion there are going to be a lot of opportunities to make some big fights, some good fights, but to be honest I'm not in a massive rush.
"I want to try and enjoy it first because it has been a long time in coming."
The 29-year-old (26-3, 19KOs) was crowned WBA super world champion in Sheffield on Saturday night after an impressive sixth-round stoppage of Fedor Chudinov.
And Groves was quick to praise trainer Shane McGuigan for his overdue success, after previous failed world title bids against Carl Froch (twice) and Badou Jack.
"Before I went with Shane I wasn't sure if I was ever going to get there, but within a short space of time working with him I knew I would be a world champion," he said.
"I always thought I was good enough but once we started gelling I knew I was going to achieve that goal. Now I need to set some new goals because I feel I can achieve so much more.
"I've been enjoying my boxing again since being with Shane. I've been winning and winning well and that's all I really want out of boxing.
"I was trying to treat this just as another fight and I was desperately trying not to think of what it would be like to be a world champion - I was petrified of that fall with me being so close in the past but never getting there.
"But of course it's a fantastic feeling for me - a lifetime's work achieved. Since I was seven years old I have wanted to become world champion and it's been a long. hard road. I've made some mistakes and in many ways I've made it hard for myself but it does make it sweeter now.
"I'm going to be such a better, more rounded human being for this victory. I can put the demons to bed - for so long I was walking round clueless as to why I was not a world champion and I was feeling sorry for myself.
"But now I can tell people I am in the best in the world because I've got a belt to prove it. It's a wonderful feeling and the weight has certainly been lifted. That thing that was there no longer is. I've learned from my losses and I think they've made me a better fighter."