West Ham and Palace are seemingly active on the final day of the window.
Bacca, 31, featured against England at the World Cup and has long been linked with a move to the Hammers, stemming back from Slaven Bilic's reign in charge of the east Londoners.
The Colombian is way down the pecking order at the San Siro, especially since Gennara Gattuso's side confirmed the signing of fellow South American striker Gonzalo Higuain in a surprise move from Juventus.
However, the report claims both the Hammers and the Eagles will miss out on Bacca, as the striker wants to return to Villarreal once again. Bacca scored 18 goals for the La Liga outfit last term.
West Ham have since signed Lucas Perez from Arsenal, while Palace have reportedly made an offer to sign Liverpool striker Divock Origi for a fee of £16.2million.