Martial is available on a free transfer following his release from Manchester United at the end of June.
Lille are among the clubs to be credited with an interest in the Frenchman, but according to Sky Sports News, there is also interest from Serie A in the shape of Atalanta.
Journalist Lyall Thomas claims that Atalanta are considering moving for Martial after learning that Gianluca Scamacca will be out for a lengthy period due to an ACL injury which was suffered during a pre-season friendly against Parma.
Martial, 28, only managed two goals in 19 appearances for Man United during the 2023-24 campaign, and he was not offered a new contract by the 20-time English champions.
The forward scored 90 times in 317 appearances for the Red Devils, though, and is certainly an attractive proposition on a free transfer considering his age and standing in the game.
Leverkusen 'identify' Matip as Tah replacement
Meanwhile, according to journalist Florian Plettenberg, Bayer Leverkusen are considering making a move for Joel Matip, who is available on a free transfer this summer following his release from Liverpool.
The 32-year-old is allegedly being tracked by a number of clubs this summer.
However, Plettenberg claims that Leverkusen are in a strong position when it comes to the race for his signature, with the Bundesliga champions potentially offering him at least a two-year contract.
Leverkusen are said to view Matip as a potential replacement for Jonathan Tah, who continues to be linked with Bayern Munich.
Matip made 201 appearances for Liverpool in all competitions, but he was restricted to just 14 outings during the 2023-24 campaign due to a serious knee problem, and the Reds decided against offering him a new deal.
Peterborough 'in advanced talks' over Susoho loan move
Elsewhere, Peterborough United are allegedly closing in on the loan signing of Manchester City's Mahamadou Susoho.
The 19-year-old made the move to Man City from Espanyol in 2017, and he signed his first professional contract with the Premier League champions in the middle of 2022.
The holding midfielder made his first-team debut for the Citizens against Red Star Belgrade in the Champions League last December, and he is highly rated by the club.
However, according to Football Insider, Susoho is set to spend the 2024-25 campaign away from the Etihad Stadium.
The report claims that Peterborough are in advanced discussions over a loan deal for the midfielder, who travelled with the Man City squad on their pre-season tour of the United States.
Susoho is expected to be a regular for League One outfit Peterborough next season if the move goes through.