The title-holder from Kazakhstan (27-0, 24 KOs) has skyrocketed up the pound-for-pound rankings over the last couple of years, destroying opponent after opponent with his crisp and clinical attacks.
And after he finished off Ireland’s Matthew Macklin in just three rounds in June, reports circulated that the 31-year-old wanted to meet St Helens man Murray (25-1-1, 11 KOs) next.
Murray’s most recent bout was a frustrating decision defeat to WBC middleweight kingpin Sergio Martinez in April, which saw the Englishman knock down the top five P4P-ranked Argentine once, with a second controversially ruled a trip.
But Murray said via his official Twitter account that claims of him turning down a ‘big money offer’ to fight Golovkin were false and that he has not been approached,.
Golovkin and his camp responded. “My first choice was Murray,” Golovkin told World Boxing News.
“My team have tried everything to get Martin for my next fight. This is boxing though and if somebody doesn’t want to fight you cannot force them to.”
Golovkin’s manager Oleg Hermann added: “I can not believe (his claim) that he did not get any information from his team at Hatton Promotions.
“Murray should really think of some new excuse as it’s really boring, what he is saying.
“If a fighter is not ready to fight, he should say ‘I need more time’ or ‘I need more fights first’ and not try to find new excuses every day.
“We had the same story with Felix Sturm, Hassan N’Dam and Daniel Geale, plus some other fighters.
“If an opponent wants to fight Gennady then the fight will happen, if they don’t want this fight, then every day you hear new excuses.”
Murray’s promoter Ricky Hatton last month suggested to ESPN’s Steve Bunce that Murray v Golovkin could well happen down the line, but wouldn’t happen straight away.
"We're hoping to make an announcement in the next few weeks,” he said. “There are lots of offers coming in for Martin, but it's just about finding the right move at the right time.
"That's something I learnt from my old promoter, Frank Warren. This promoting game is all about timing and Martin's a real flavour of the month due to his wonderful performance.
"He's had offers - Golovkin [was] one of them. Martin has no fear of fighting any of them and I think he's proved that by going to Argentina and going to Germany.
"I wanted to fight Kostya Tszyu three years before I boxed him and if I'd done that, he'd have beaten me," Hatton admitted. "It's all about the right timing - build the fight up, build the interest."
Murray has applied for a US visa, which if successful could lead to further developments on the Golovkin fight front sooner rather than later.