The 27-year-old defender, who already has one goal and two assists in Chelsea's opening four Premier League matches, impressed in the Blues' 2-0 win over Bournemouth and was the closest out of anyone to breaking the deadlock in the first half when his right-footed shot struck the post.
He was also involved in the build-up for both Pedro and Eden Hazard's goals as Chelsea finally got the better of the stubborn Cherries defence.
Alonso's impressive start to the season has seen him named in Luis Enrique's Spain squad for the matches against England and Croatia later this month.
Sarri said: "Alonso, at the moment, in this position at left-back is maybe the best in Europe.
"[His] physical qualities are at a top level, I think. He's doing very well in the offensive phase.
"But I also think he can improve in the defensive phase. If he improves that, he could be the best left-back in the world."
Alonso joined Chelsea in August 2016 from Fiorentina and has gone on to make 86 appearances in all competitions, finding the back of the net 15 times. The Spaniard has had an unusual career path, which has seen him turn out for the likes of Real Madrid, Bolton Wanderers and Sunderland.
Speaking about the Bournemouth game, Sarri said: "I am happy with the result and I am happy with the performance.
"It was a very difficult game. [Bournemouth] are very organised defensively, and defended very well. In the first half, the situation was difficult.
"Maybe we needed to move the ball at another speed, and maybe more movements without the ball. But in this kind of match, usually you can win in the last 20-25 minutes, so I was always confident."