Reports claimed Chelsea always wanted to keep the winger at Stamford Bridge but the player himself was understood to be keen on a move.
And it seems Hazard is not going to leave Chelsea this summer as he prepares to return to training with the Blues today.
Courtois, who wants to join Real Madrid, was handed an extended holiday after following his involvement with Belgium at the World Cup.
Earlier, TUKO.co.kehad reported how Manchester United are said to be targeting Chelsea winger Willian in a stunning deal for the Brazil global.
Sarri was appointed three weeks ago after Antonio Conte was sacked as head coach and Chelsea were well beaten by Manchester City in Sunday's Community Shield at Wembley. "If Courtois says the same, I have to speak with my club because I only want players with a high level of motivation".
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The head-to-head battle is scheduled to take place in November at Shadow Creek. Told about the idea later, Woods said: "I'm definitely not against that".
He is optimistic of a strong campaign, which begins with Saturday's Premier League opener at Huddersfield.
However, the Nigerian global is not sure of pinning down a shirt under Sarri, who favours a different tactical system.
Courtois, 26, has a year remaining on his contract and has been repeatedly linked with a move to Real Madrid.
Riyad Mahrez to Manchester City from Leicester. I would like to know if Courtois would tell me the same thing.
"The results I'm sure will come, because we're good players. That is behind me now, and I'm feeling strong and ready to go".
And Willian, who has been with Chelsea since 2013, has now committed his future to the west London club. "In the next week we have a friendly match [against Lyon on Tuesday] and I prefer in this moment to be on the pitch with the players for training".
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