The Spaniard has been at the centre of transfer talk, having played just 32 minutes in the Premier League under Antonio Conte this season.
Fabregas was given a chance in the EFL Cup on Tuesday and netted a match-winning brace in a 4-2 victory over Leicester City.
The 29-year-old said moving away from Stamford Bridge was never a consideration.
"I never planned to leave Chelsea," Fabregas told Cadena COPE.
"Real Madrid? Maybe they called me or maybe not. But I didn't think to leave Chelsea, not even for a second."
Fabregas said he was growing tired of the speculation over his future, insisting he wants to stay despite a lack of game time.
"I'm tired of the news that says that I'm offering myself to other clubs. I'm one more of the team and I will keep fighting to play here," he said.
"If I knew that I have no level to play in this team, I would leave, but I'm happy here. It hurts a lot not to play, but I know that I have enough level to play here and I will give my best."
He added: "I spoke with Conte. We like him very much, he's a great coach, very hard and he says the things very clear. We are very happy with him."
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