The Juventus midfielder damaged his meniscus in one of his first training sessions with his new club late last month while they were on tour in Los Angeles.
Surgery would rule him out of the Qatar World Cup from November 21 - December18 and Pogba, who has 91 caps for his country, would instead opt for "conservative therapy".
Italy’s Tuttosport said the regime would consist of three weeks in the gym and swimming pool then two weeks of individual work. All going well, Pogba would return in time to be able to prepare for the World Cup where France start their campaign against Australia in Doha on November 22.
French sports daily newspaper L’Equipe said on Wednesday that his decision had put him on a collision course with his new club, who wanted him to undergo surgery and miss the World Cup so that he could return fit for them in the second part of the season.
Pogba returned to Juventus after several tumultuous seasons at Manchester United.
