Real are set to announce the capture of the Belgian forward, 28, after Chelsea have played Arsenal in the Europa League final on May 29.
Hazard helped them to a top-four finish with 16 Premier League goals and 15 assists in 2018-19 and he could yet deliver a final piece of silverware before saying goodbye.
Despite an encouraging season under Sarri, the Italian remains under pressure and some reports suggest he might not be in the post by the start of next season.
However, Hazard believes sacking him would be a mistake and insists they have made progress under the former Napoli chief.
“I think if they can keep the same philosophy as this season, keep playing football like we tried to do it this season, but in a better way – that’s it,” he said when asked how they can improve.
Despite finishing third, Chelsea ended the campaign a whopping 26 points behind champions Manchester City and 25 behind Liverpool in second.
“When you look at the season they are far better than us, Manchester City and Liverpool,” Hazard added.
“If we want to compete with them next season, we need to do it better. It’s that simple. We need to win games in football. If you don’t, you’re in trouble.
“Yes, it is one of my best [seasons] in terms of goals contribution, of course.
“But at the end of the season, you want to win trophies, so we can go to Baku and win a trophy.
“If we do that and finish in the top four, it’s still a great season.
“Now it’s like six-and-a-half [out of 10]. If we win in Baku it is going to be maybe seven-and-a-half.”
After Chelsea drew at Leicester 0-0 on the final day of the season, Sarri revealed he hoped to still be in a job but admitted he was not entirely sure about where his future lies.
“I think so, but I am not sure,” he said when asked if he will be in the dugout next term.
“I can say only that the club asked me for the Champions League, and we reached the target.
“As you know very well, I love English football. I love the Premier League; it’s fantastic and the level is the best in the world, I think.
“The atmosphere in the stadiums is wonderful. I would like very much to stay here.”