Edmund has been Murray's training partner during the off-season, with the three-time grand slam champion inviting him to training blocks in Miami and most recently Dubai.
"Kyle really deserves what he is now achieving because he has never shirked from the hard work," Murray told British media. "Being selfish, I would be delighted if he continues to link up with me in my winter training block.
"He is the perfect practice partner. He will always be welcome but I think it's time he started thinking about himself and what his specific needs are from a training block in the off-season, rather than happily going along with mine.
"He has an excellent coach in Ryan Jones and a good back-up team. Now Kyle is a top-50 player he's got to become more self-centred in his outlook and really identify what he personally needs to work on."
Murray, who beat Edmund en route to his 40th career singles title at the China Open in Beijing on Sunday, is bidding for his third Shanghai Masters title when he faces American Steve Johnson in the second round of the tournament.
