Edmund has been Murray's training partner during the off-season, with the three-times 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 said. "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."
Edmund recently booked his place in the second round of the Shanghai Masters with a three-set win over Argentina's Federico Delbonis on Monday.
The British number two had battled through two qualifying matches to reach the main draw but showed no ill-effects as he finished strongly to triumph 6-3 5-7 6-4.
Edmund also reached the quarter-finals of the China Open last week where he was beaten by compatriot Andy Murray, and rose into the world's top 50 as a result.
The 21-year-old will face a major test in the second round of the Shangai Masters where he will come up against reigning US Open champion and tournament third seed Stan Wawrinka.
As for Murray, the Scotsman is bidding for his third Shanghai title when he faces American Steve Johnson in the second round of the tournament.