Sky Sport Italia claim that Atalanta accepted a €15m offer from Fenerbahce for Mario Pasalic, but the Croatia international turned it down.
The Turkish team has already plucked players from Serie A this summer, picking up Edin Dzeko as a free agent after his contract with Inter ran down.
According to the Italian television station, another proposal worth circa €15m was presented to Atalanta for Pasalic and the two clubs were in basic agreement.
However, the 28-year-old is not interested in such a move and remains eager to continue his career in Bergamo.
Pasalic first came to Italy on loan at Milan in 2016-17 from Chelsea, then was sold to Atalanta for a total €17m following an initial two-season loan spell.
He made 33 competitive appearances for La Dea last season, contributing five goals and two assists.
The reports state that this was not just a rejection of the Fenerbahce option, but also Pasalic is determined to remain with Atalanta.