Zapata has been on Newcastle’s shortlist of strikers as they look to bring in another forward after adding Chris Wood from Burnley last week.
Newcastle failed with an initial bid, which included a €5m loan fee and €18m purchase clause conditional on them surviving in the Premier League this season.
Atalanta wasted little time in rejecting the offer but it has been claimed Newcastle are preparing to table another offer soon.
According to Italian outlet Tutto Mercato, the Serie A club are expecting to soon see another offer from the Magpies.
The next bid is expected to be close to the €40m Atalanta want before they would agree to sell him.
The Italian club have no problem in accepting a loan offer for the Colombian if the purchase clause has no conditions attached to it.
Atalanta are in no mood to accept any offer that would not be a guaranteed sale of Zapata.
The forward is Newcastle’s priority attacking target but they are wary of spending big on a player who could become a luxury in the Championship next season if they are relegated this season.