Midfielder Murray, who has been at Field Mill since 2010, has not featured in the Stags' last two games.
Cox insists that, although he has agreed to grant Murray's request of a short-term move away, the 31-year-old remains a big part of his plans.
"After training on Thursday, Adam approached me and asked if he could go out on loan to get first-team games and competitive football under his belt," Cox told the club's official website.
"Any team in the world would want a fit and strong Adam Murray in their side and I've had conversations with the player regarding the fact that I would like him to work hard, gain his place and come back to captain the side for another successful season.
"I have the unenviable task of trying to keep a whole squad of players happy, which at times is very difficult as I know I have players who are so desperate to play."
Murray was one of the stars of Mansfield's promotion-winning campaign last season. His performances led to him being named in the Non League Paper's Blue Square Bet Premier Team of the Year, which was selected by reporter Stuart Hammonds.