But now that Fulham are on the brink of relegation we are not sure that the 33-year-old would want to move to Craven Cottage during the summer.
Sarri, buoyed by Wednesday's 2-0 win over Tottenham four days after the freaky climax to the Carabao Cup final, believes the furore around Kepa Arrizabalaga's behaviour has galvanised his squad.
"We are very happy for Willy, because now we know very well he's able to play also in a very hard match", Sarri said.
"Now I am in the first season in England, and I started to understand some things, not everything at the moment, so now I realise that here it [takes] longer, more hard".
"So I think he needs to improve in the physical condition - especially the acceleration - and then he will be able to score of course". "I understand what is at stake and that it's a London derby against a very, very good football team", he said.
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"But in this moment we know that Willy is doing very well".
So far the defender has played in just seven games for the club and all of them have come during the first half of the season and he hasn't made a single appearance in over three months.
"I think that he played very well in the last match [against Tottenham], better in the second half than in the first half".
Asked about Ranieri's departure, Sarri said: "I'm really very sorry. So we need to value the recovery because we ran for 15km on Sunday on average, and the average in the last match was 12km", Sarri added.
Chelsea are seemingly locked in a battle for fourth place with Manchester United and Arsenal - although Tottenham could be drawn in - and Sarri understands the club's expectation is that he delivers Champions League football. For him, it's very important to finish the match in that way.
With Fulham 19th in the Premier League and ten points from safety, survival is nearly certainly beyond them but Parker is determined to make an impact during what he...