According to Tuttomercatoweb, the bid from Fulham is worth around €19 million (£17.2m).
Furthermore, the 27-year-old defender has been offered wages of around €2.5 million per season (£44,000-a-week) and it will be interesting to see if the Italian outfit are willing to accept the offer from the Londoners.
Fulham have been vulnerable at the back since the start of the season and they need to solve their defensive issues if they want to stay up this season.
Berat Djimsiti is a quality defender and he could improve Fulham immensely.
Convincing the player should not be too difficult for the London club but Atalanta might not be keen on selling the 27-year-old this late in the window.
Even if they are getting good money for Berat Djimsiti, they will struggle to find a quality replacement with so little time left.
It remains to be seen how the situation unfolds in the coming hours and whether Scott Parker is able to get his man with just two days remaining in the window.