The England midfielder made something of a slow start to life at Stamford Bridge after having arrived at the west London club from Everton in the January transfer window.
However, Barkley seems to be winning over the new man in charge at Chelsea FC, and he has been in solid form for the Blues to help them make a strong start to the Premier League season.
Indeed, the 24-year-old has now scored three goals and made three assists in nine Premier League appearances for the west London side to help them keep pace with Liverpool FC and Manchester City at the top of the table.
Barkley scored one and set up two as Chelsea FC claimed a dominant 4-0 victory over Burnley at Turf Moor on Sunday afternoon.
And new Chelsea FC boss Sarri has admitted that he has been thrilled by the strong start Barkley has made to his Chelsea FC career.
Speaking at his post-match news conference at Turf Moor on Sunday, Sarri said: “Barkley is doing very well. In this period, he is playing really very well.
“He has improved very much in the defensive phase. He has improved his physical condition. Last season was very difficult with a very serious injury.
“He is a very good player from the technical point of view. Now I think Ross is complete.”
Barkley will be hoping to feature for Chelsea FC and continue his fine form when the Blues take on Derby County in the fourth round of the League Cup at Stamford Bridge on Wednesday night.
The Blues will then take on Crystal Palace at home in the Premier League on Sunday.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news