But Londoner Groves, 25, complained the Manchester fight was ended too soon.
Mike CostelloBBC boxing commentator
"After all the wrangling in the media and behind the scenes, money and egos have combined to bring them together again for the most eagerly awaited rematch in British boxing since Nigel Benn met Chris Eubank for the second time two decades ago.
"Froch's win against Groves last November ended controversially and many say prematurely when referee Howard Foster intervened to stop the fight in the ninth round.
"Groves was ahead on all three judges' scorecards, having floored the champion in the first round, and his appeal to the IBF last month led to the governing body ordering the rematch. Froch was left with a choice: Give up the title or give Groves a second chance."
"A rematch is the last thing he should want to do," Groves told
BBC Radio 5 live.
"There's nothing for him to cling onto to take to the next fight."
Froch admitted he considered retirement "for two or three days" following the fight but now says he cannot wait to return to the ring and "do a job" on Groves.
The bout is the biggest rematch in British boxing since Chris Eubank fought Nigel Benn for a second time at Old Trafford in 1993.
There were bitter recriminations in the wake of the first fight between Froch and Groves at the Manchester Arena.
Groves led on points after flooring the champion in round one but referee Howard Foster stepped in to halt proceedings when Froch went on the attack in round nine.
With Froch angling for a rematch with American Andre Ward or a fight against Mexican Julio Cesar Chavez Jr in Las Vegas, it looked as though Groves might have to wait for his chance to avenge the loss.
He said: "I am trying to get it on at the City Ground because there are two things I want to do before I retire; one is fight at the City Ground and the other is fight on the Vegas strip.
"But one fight at a time, and if I can get this fight at the City Ground, that would be phenomenal.
"We don't like each other, let's make no bones about it.
"It is quite personal and when you have a domestic fight where two people don't like each other, they have already boxed and it could have gone either way, and the stoppage was a bit ropey, it just makes for a massive event."
Froch's victory in the first fight took his career record to 32 wins from 34 fights, while defeat for Groves was his first in 20 professional outings.
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