The Ligue 1 side are expected to sell Tanguy Ndombele this week, with Tottenham in pole position to land the midfielder.
Lyon will receive an initial £55m for the France international and plan to reinvest some of the proceeds back into their squad.
New manager Sylvinho is keen to strengthen the team’s defence and has identified Bailly as his principal target.
The Ivory Coast international was restricted to just eight Premier League starts in an injury-hit season last time out.
If Lyon are unable to acquire the United stopper, they could turn their attention to Arsenal’s Laurent Koscielny.
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