France Under-21s international Caqueret was reportedly of interest to the Rossoneri, who are aiming to win Serie A this season for the first time since 2011 - it holds a two-point lead over rivals and defending champions Inter heading into the final two games of the season.
Milan is, however, set to lose midfield powerhouse Franck Kessie on a free transfer ahead of next season, with the Cote d'Ivoire international reportedly set to join Barcelona.
As such, Milan will be hoping to line up a replacement, and 22-year-old Caqueret had apparently piqued their interest, with his contract at Lyon winding down.
But any hope of a free transfer has now been dashed after Caqueret agreed to a new deal, set to keep him at Lyon until 2026.
Having come through Lyon's academy, Caqueret has already played in 88 games for the French side. He has made 29 Ligue 1 appearances and played eight times in the Europa League this season.
Caqueret has attempted a team-high 70 tackles in Ligue 1 this campaign, winning 39 (55.7 per cent), while no team-mate can better his 40 interceptions. Though he has failed to score or assist, he has created 24 chances for others.
While Caqueret's extension is a positive move, it has been a disappointing season for Lyon domestically, and they sit eighth in Ligue 1 with two games remaining.
With European qualification looking unlikely, the future of fellow midfielders Houssem Aouar and Lucas Paqueta may well lay elsewhere, with Bruno Guimaraes having already left for Newcastle United earlier this season.