The 32-year-old is believed to be keen on a move to Serie B outfit Sampdoria to join up with former coach Walter Novellino, who he played under at Piacenza.
Atalanta are thought to be willing to let Gautieri leave Bergamo, but the deal is being held up as both clubs cannot agree a fee for his services.
Sampdoria have offered Fabian Valtolina in exchange for Gautieri, but Atalanta are unwilling to accept the deal as they want a straight cash transfer.
