The Spanish international has been linked with a move away from Stamford Bridge this summer after performing consistently well for the Blues since he joined in 2016.
However, Sarri has insisted the player not get ahead of himself and says there are significant improvements Alonso can make.
He said at the Chelsea news conference on Friday: “He [Alonso] is a very good player and can improve in the defensive phase.
“Of course (I have told him). He has physical qualities at the top level.
“I think that he can do more in the defensive phase.
“He is a good player in both, but I think he can do more.”
Alonso has so far played a key attacking role in Sarri’s new system at Chelsea, in particular providing the assist for Pedro for the opening goal in Chelsea’s 3-2 win over Arsenal in August.
He has consistently performed well for Chelsea with his attacking movement from the left-back position but he is not particularly known for his defensive attributes.
Chelsea’s defence has been questionable this season, despite the fact that the Blues have taken maximum points from their opening three games of the season.
Sarri will see this as an area of improvement and amid rumours of a move away, he has sent a message to Alonso to not let the speculation go to his head.
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