The Bergamo club have followed up on their interest in the 23-year-old by entering formal discussions to sign him.
Senesi had an excellent first season in Europe after his move to Feyenoord from San Lorenzo.
His form led to Feyenoord having to reject a €15m bid from Sevilla for the Argentine.
Feyenoord want at least €20m to part with Senesi, who they shelled out a club-record €7m for.
Atalanta are in ‘open negotiations’ to sign Senesi, although there is nothing concrete in place yet.
The next few weeks will be decisive, but in the meantime Senesi is preparing for the start of the new Eredivisie season with Feyenoord.