The Toffees are hurriedly looking around for new attacking options to bring to Goodison Park and have zeroed in on Zapata.
A loan offer is set to be put to Atalanta for Zapata, according to Sky Italia, but it will be rejected.
The Serie A club are prepared to let the 31-year-old move on this month, but they will only consider a permanent transfer.
Whether Everton are willing and able to present a bid which will convince Atalanta to sell Zapata remains to be seen.
Zapata has only scored once in Serie A so far this season, in 12 outings.
The striker has been prolific in the Italian top flight though, notching 107 goals in 269 outings in the league.
Zapata has 18 months left on his contract at Atalanta, who he linked up with in 2018, initially on loan, from Sampdoria.
