Cristante's performances this season are understood to have drawn the attention of a number of Europe's biggest clubs, with the 23-year-old having scored 12 goals in 45 appearances across all competitions.
Sky Sports News reports that the two-time Italy international is keen on a move to England, which is understood to have piqued the interest of Arsenal and Chelsea.
Cristante's representatives reportedly met with Premier League clubs in London earlier this week to discuss a possible move, although teams in Italy and Germany are also thought to be monitoring the situation.
Arsenal and Chelsea could face competition from Borussia Dortmund for the midfielder's signature, while there is also interest from some of Serie A's biggest clubs.
Cristante came through the ranks at AC Milan before joining Benfica, but he spent time out on loan after moving to Portugal and made his move to Atalanta permanent earlier this year.