Martial is expected to be on a relaxed move following his departure from Manchester United at the end of June.
Lille are among the clubs believed to have interest in the Frenchman, but according to Sky Sports News there is also interest from Serie A in the form of Atalanta.
Journalist Lyall Thomas claims Atalanta is a move for Martial after learning that Gianluca Scamacca will be out for an extended period of time due to an ACL injury suffered in a pre-season friendly against Parma.
Martial, 28, scored just two goals in 19 appearances for Man United in the 2023-24 campaign, and the 20-time English champions have presented him with a new contract.
However, the striker has scored 90 goals in 317 appearances for the Red Devils and, given his age and position in the game, is a hot proposition for a relaxed move.
Meanwhile, according to journalist Florian Plettenberg, Bayer Leverkusen are considering making a move for Joel Matip, who will be free this summer following his departure from Liverpool.
The 32-year-old is reportedly being followed this summer by several clubs.
However, Plettenberg claims that Leverkusen are in a position to compete for his signing and that the Bundesliga champions could offer him a contract of at least two years.
Leverkusen are reportedly considering Matip as a possible replacement for Jonathan Tah, who remains linked to Bayern Munich.
Matip made 201 appearances for Liverpool in all competitions but was limited to just 14 games in the 2023-24 campaign due to a serious knee problem and was not offered a new contract by the Reds.
Elsewhere, Peterborough United is reported to be the latest to sign Mahamadou Susoho on loan from Manchester City.
The 19-year-old left Espanyol for Man City in 2017 and signed his first contract with the Premier League champions in mid-2022.
The midfielder made his first-team debut for the Citizens against Red Star Belgrade in the Champions League last December and is highly valued at the club.
However, according to Football Insider, Susoho is expected to spend the 2024-25 campaign away from the Etihad Stadium.
The report claims that Peterborough are in complex talks over a loan deal for the midfielder, who travelled with the Manchester City side on their pre-season trip to the United States.
Susoho is expected to be a regular at League One Peterborough next season if the move goes through.