The Belgian striker was linked to the Premier League side, who now have eyes on Timo Werner from RB Leipzig.
Mertens is a veteran with Belgium and Napoli, and is now looking likely to stay with the Italian outfit.
He is likely to sign a new deal, but was convinced of the Chelsea project in January, per Belgian journalist Kristof Terreur.
"In January when Chelsea knocked on the door, he was quite convinced," Terreur told BBC Radio 5 Live.
"But once you are in the south of Italy, with good money and you are a god, why would you change that?
"He would come to the Premier League as a nobody and in Italy he is a star."