According to De Telegraaf and other Dutch sources, Atalanta have made an approach for the 23-year-old.
Furthermore, Lammers and his agent want PSV to let him join last season’s third-placed team in Serie A.
These developments have irritated PSV because Lammers had a verbal agreement in place for months to sign a new deal.
Several clubs have expressed their interest in Lammers, but Atalanta’s is the most concrete.
Atalanta want to pay €7m for Lammers, but PSV are looking for a ‘double digit’ fee of €10m-plus.
The Eindhoven club do not intend to make it easy for Lammers and his agent Reza Fazeli, but will accept a good offer.
Lammers is out of contract in a year’s time and if he does not renew, PSV know they have to cash in now.
PSV boss Roger Schmidt favours pairing young English prospect Noni Madueke with Donyell Malen up-front, so Lammers is not guaranteed a start.
Lammers spent the 2018-19 season on loan at Heerenveen, scoring 19 goals in his 35 appearances.
A serious knee injury kept him out of action until late January last season, limiting his involvement.
After his return, Lammers scored two goals in seven Eredivisie appearances for PSV.