According to Scott Wilson from The Northern Echo, the Magpies have already agreed on a fee with Lille for Botman, who has been earmarked as their priority target this summer, as they want to improve their defence ahead of the coming season.
The report adds that Newcastle will pay an initial fee of around £30 million for the 22-year-old centre-back, with them also agreeing on numerous add-ons that could potentially be costly.
While Milan have held their own discussions with Lille's management and Botman's representatives, the Rossoneri have effectively concluded their pursuit of the Dutchman, with them being unwilling to match Newcastle's terms.
The only discussions ongoing remain between Newcastle, Lille and the Dutch centre-back.
While Paris Saint-Germain were seen as potential suitors in the French press, as things stand the Ligue 1 champions are yet to make an approach to Lille.
PSG's interest could complicate things for Newcastle, and so the Magpies are determined to finalise things in the coming days, after Botman completed his international duties with the Netherlands Under-21s on Saturday.
Newcastle's recently-appointed Director of Football, Dan Ashworth, was among those watching Botman at Llanelli's Parc-Y-Scarlets.
Ashworth is set to lead this week's negotiations, with the hope for Newcastle being that a deal can be concluded ahead of next weekend.
While Botman was set to join Newcastle in January, Lille rejected a number of offers from the Magpies.
If a deal is completed, Botman would become Newcastle's second signing of the summer, after completing a quickfire deal for Matt Targett for £15 million from Aston Villa last week.