Mauresmo, who would have been the first women s captain of France s men s tennis team, was appointed in June to take over from Yannick Noah in 2019, when the Cup will be played under a new single-week format in Madrid.
Noah led France to three Davis Cup victories ended his third spell as captain in November with defeat to Croatia in the final.
Mauresmo, a former World No.1 and double Grand Slam winner, led France s women s team to the final of the Fed Cup in 2016. She has also coached Andy Murray.
The 24-year-old Pouille reached No. 10 in the world in March but the French player has since fallen back to 32nd.