The midfielder has been heavily linked with a move away following the club’s relegation to the Championship last season.
While he was one of several disappointing performers in that campaign, his stock rose considerably this summer as a result of his fine performances for France at Euro 2016.
Several Premier League sides have been linked with a potential move, but La Liga giants Real Madrid seem his likeliest destination with Diario Madridista claiming formal negotiations had been opened last week.
The French midfielder has made it clear he wants to leave, but has urged Newcastle fans to understand that desire.
Sissoko's stance has angered Newcastle supporters, but he added: "They need to understand, I spent three and a half years here.
"I gave everything for this club and I want to play some big games. For that I need to go somewhere else.
"I want to play in the Premier League, I want to play for a big club who can get into the Champions League. That's why I said I want to leave this year.
"I've spent a lot of time here and now it's time to look forward. The fans need to understand my situation, I hope they will and that everything will be OK."