Sissoko, who joined the Magpies from Toulouse in 2013, was unable to help them avoid relegation to the Championship last season and is keen to move on.
Newcastle boss Rafa Benitez is ready to grant the France international his wish, but the club want £35m for the midfielder.
Inter, with new boss Frank De Boer in charge, are now keen to do a deal following his impressive performances for France at Euro 2016.
Sissoko, 27 has been on the radar of Real Madrid, Borussia Dortmund and Arsenal, but the Italian giants are hopeful of clinching his signature.