The 21-year-old, already regarded as one of Italy's brightest defensive talents, was a priority for the Premier League side in the closing days of the market.
Italian journalist Matteo Moretto reported that Newcastle made multiple enquiries but never entered formal negotiations after Atalanta made clear that Scalvini was not for sale. La Dea are understood to have placed a minimum valuation of around 50 million euros on the centre-back, a figure that deterred further bids.
New head coach Ivan Juric has underlined Scalvini's importance to his plans in Bergamo. "Giorgio is central to what we want to build here. He represents both the present and the future of Atalanta," Juric has said.
Club officials have also stressed that they see him as a cornerstone of their project as they aim to compete strongly in Serie A and in Europe this season.
Napoli were also credited with an interest in the Italian international earlier in the window, but they instead secured Bologna defender Sam Beukema. Newcastle eventually shifted their focus to AC Milan's Malick Thiaw, who joined the Magpies in a deal worth around 40 million euros.
Scalvini, who came through Atalanta's academy, has already made more than 80 senior appearances despite his age and featured regularly for Italy under Luciano Spalletti. His development has attracted consistent attention from abroad, but Atalanta have remained resolute in their stance.
With Juric at the helm, Atalanta have made a strong start to the new Serie A campaign, and Scalvini has been a commanding presence at the back. For now, Newcastle and other admirers will have to wait, as Atalanta remain determined to keep one of their prized assets.