Groves has longed for another opportunity to fight Froch after their first encounter ended in controversial circumstances, but Froch has released a statement saying that the Londoner has opted not to accept a lucrative fee to fight for his two world titles.
A statement from Froch read: "There has been plenty of speculation over the last few weeks regarding my future. As it stands, we are looking closely at two options - George Groves and Julio Cesar Chavez Jnr.
"Yesterday, we made a seven-figure offer to George Groves for a second fight that would have seen him earn around double that of the first. Disappointingly, George rejected this offer, so we are continuing our talks with Top Rank and HBO regarding Chavez Jnr.
"I understand the demand for the Groves fight in the United Kingdom, but also the demand in the United States for the Chavez fight. Talks are ongoing and no doubt some further news will break soon."
Groves revealed earlier this week that he had appealed against the decision to stop the fight in the ninth round in an attempt to be named the mandatory challenger for Froch's IBF belt for a second time.