Well, Sky Sports say that the Blues, along with Premier League rivals Arsenal, are considering making a move for the 23-year-old following an impressive season for the Serie A outfit.
Sky Sports report that even though the midfielder only made his loan move from Benfica to Atalanta permanent earlier this year, he could be on his way out at the end of the campaign with the player keen on a move to England and his representatives holding talks with potential suitors in London earlier this month.
The 23-year-old has certainly made a big impression for the Italian club, scoring 12 goals and providing a further four assists in 44 appearances in all competitions.
His form was so good that he earned a call-up to the Italy national team, and as well as showing the impact he can make in the final third – he has made 52 key passes in 42 games in Serie A and the Europa League this term, as per WhoScored.com.
But he has also shown that he can make a defensive contribution too, having won 78 tackles and made 26 interceptions, as well as winning 110 of the 205 aerial duels he has faced.
It’s difficult to say.
While he has made a big impression with Atalanta, the Blues need to be sure that he is at a level that he can make a big impact for them in the Premier League title race and in Europe in the future, and he might not have the quality to do that.
If the west London outfit are going to sign a new player for the central midfield area this summer they need to make sure that they would be an upgrade on the likes of Danny Drinkwater and Ross Barkley.
If they get Cristante they would potentially be making the same mistake that they did with former Leicester City man Drinkwater, who Chelsea fans on Twitter want to be sold this summer, with his move to Stamford Bridge not really working out.