Ligue 1 side Lyon are on the lookout for a centre-back and have made Bailly their leading target.
The Ivory Coast international endured a frustrating season last time out, making only eight Premier League starts in an injury-hit campaign.
And Lyon hoped that they would be able to prise him away from Manchester ahead of next season.
However, Bailly is not thought to be enthusiastic about the prospect of moving to the Groupama Stadium.
Lyon are now expected to turn their attention towards other targets.