The duo split on Monday after Murray's loss in the final of the Madrid Open against No.1 Novak Djokovic a day before, which dropped him to third in the rankings.
The partnership between Amelie and Murray saw the Scot regain the number two slot in the rankings earlier. But he failed to win a single Grand Slam during their association that began in 2014.
"It doesn't have to be, but it's definitely possible it could be an ex-player," Murray was quoted as saying by the BBC on Tuesday.
Prior to Mauresmo, Murray worked with Ivan Lendl, who guided him to US Open, Wimbledon and Olympic success.
Murray believes coaches who have played top-level tennis can "help around the Slams, in the big moments, the big matches".
"They've been there and done it and they understand that," added the 28-year-old.