The Liverpool forward won the Golden Boot last season and Sarri is backing Hazard to dethrone the Egyptian this campaign.
Chelsea sit top of the table as a result, and Hazard already has five goals to his name - three more than Mohamed Salah.
"I want to speak with him and I want to speak to the doctor and then I will decide. He has to improve some things, but he can do it", the Italian is quoted as saying by Sky Sports after Hazard scored a hat-trick against Cardiff over the weekend.
His best total came in 2014-15 when he scored 19 goals, and he scored 17 times in each of the past two seasons.More news: NCDOT warns residents about Florence flooding interstates, highways
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"I think Hazard can improve more", Sarri added.
Chelsea are ahead of Liverpool on a goal difference of one, and two points in front of champions Manchester City.
"I think when you throw that in the mix, he's one of these that you probably need to keep educating, keep testing him with regards to can you improve him, but also as well make sure you tell him on occasions, we all do as human beings, how well he's doing". I think it's normal that in this period we have some defensive problems.
However, according to Giroud, his colleague still has a big part to play for Chelsea, with both men vying for a starting spot in Sarri's line-up, as he told reporters on Monday: "It has always been a fair competition between us and we will both try to step up to help the team reach our target". In his second coming at the West London club, the Brazilian global has gone from being one of the first names on the team sheet to being a peripheral figure to now becoming a regular once again, all in just two years.
'It's very hard. The gap last season was 30 points so I think to go above 30 points in one season is very, very hard.