Maitland-Niles left Arsenal for Lyon in the summer of 2023, and the 28-year-old contributed two goals and four assists in 42 appearances across all competitions for the French club last season.
He is under contract at Lyon until the summer of 2027.
Foot Mercato now reports that Maitland-Niles could return to the Premier League this summer, with sources in England linking him to a move to Crystal Palace.
Palace finished 15th in the Premier League last season but won the Conference League, securing Europa League football for the upcoming campaign.
Pierre Sage has been named new manager at Palace after the departure of Oliver Glasner.
Sage arrives most recently from Lens, but before that spent time at Lyon, where he managed Maitland-Niles directly.
Earlier in his career, Maitland-Niles has also played for Southampton and Roma.
The 28-year-old has previously won five caps for England's senior team, and the prospect of working under a familiar face in Sage at Selhurst Park could prove decisive in any move back to English football.
Maitland-Niles began his career at Arsenal, coming through the club's academy and making more than 100 appearances for the Gunners before a series of loan spells, including at Southampton and AS Roma, eventually preceded his permanent exit to Lyon two years ago.
His versatility across multiple defensive and midfield positions has long been considered one of his greatest assets, a quality that could appeal to Palace as they prepare to juggle Premier League and Europa League commitments simultaneously next season for the first time in the club's history.
Should the move materialise, it would mark a return to regular Premier League football for a player who has spent the past two years rebuilding his career in Ligue 1 after a difficult final period at Arsenal.