Police received a tip-off about the terrifying plot and passed it on to Groves and his fiancée Sophie, according to The Sun.
The 23-year-old, who became a household name when he defeated James DeGale in a sell-out fight at the O2 arena last year to win the British super-middleweight title, was due to face Kenny Anderson on Friday but had to pull out with a back injury.
A police spokesperson said: "We can confirm a threat to the welfare of a man was made to police in Hounslow."
However, Groves management team said his decision to pull out of the fight had nothing to do with the "alleged threats".
A source told The Sun that: "George and Sophie were told by CID officers a threat had been made on his life and they should consider their safety. The intelligence said if he wasn't shot before the fight, it would happen in the ring."
Groves's fight with Anderson would have been a rematch of their contest in November 2010 which Groves won in the sixth round.
The Sun said that there was "no sign" of Groves or his fiancée in their flat but added that police said they were not in protective custody.
In a statement Groves apologised for having to pull out of the Anderson fight but made no reference to the alleged threats.
"I am sorry to confirm I have had to pull out of my scheduled fight this Friday due to injury. I hope for a quick recovery but it just won't be in time for this week," he said.
"I truly apologise to everyone who has spent money and made plans around getting to the fight. I really don't want to compromise myself and under-perform because I am not 100 per cent fit."