Earlier this month, Cotto floored Sergio Martinez four times on the way to winning the WBC title, but Murray, who will need to beat Max Bursak in Monte Carlo this evening to keep his world title hopes alive, has insisted that the 33-year-old's performance was over-rated.
The 31-year-old is quoted by Boxnation.com as saying: "I know that I could definitely beat Cotto. He didn't dethrone the same Sergio Martinez that me or Julio Cesar Chavez Jr fought.
"I'd also like Cotto because he's got the WBC belt that I believe should already be mine, and never forget boxing is also business. That's where the most money is."
Murray's previous attempts to win a world title have seen him draw with Germany's Felix Sturm before going on to lose on points to Martinez in Argentina in April 2013.