Golovkin, 31, is on the lookout for another victim after handing Matthew Macklin the worst beating of his career last weekend and hopes two-time world title challenger Murray can cut through some potential red tape to accept the deal on offer.
“Gennady has already said that he wants to fight Martin Murray next,” manager Oleg Hermann told World Boxing News.
“The problem is, we are told that Martin has big problems with his US visa and cannot go to America.
“If he can get his visa and wants this fight, we have an HBO date on November 2 and we can make this big fight happen at Madison Square Garden.
“As yet, we have had no answers back from Murray or his team on this matter.”
St. Helens-based Murray recently pushed pound for pound-ranked WBC champion Sergio Martinez all the way in a spring trip to Argentina and was unlucky to come away from the fight without his undefeated record.
As Golovkin harbours hopes of a big-money battle with Martinez, a clash with 30 year-old Murray looks to be the next best thing as ‘Maravilla’ is out of commission until 2014 following a serious knee injury.