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Fabregas, 27, left Barcelona to join the Blues earlier this week in a transfer worth a reported 33 million euros plus extras, signing a five-year deal.
There was a clause in the Spain international's Barca contract that entitled former club Arsenal to a first refusal on a player who spent eight years in North London.
However, Fabregas says Gunners boss Arsene Wenger turned down the opportunity to sign him as the club already had enough cover in his position.
"When I decided that my time at Barcelona had ended, I looked for the best option for me," Fabregas, currently on World Cup duty with Spain, told a news conference in quotes picked up by the Guardian.
"Arsenal was the first option, for contractual reasons. There was a clause that gave them the right to decide.
"We spoke to Wenger and he said that the space was very well filled by Mesut Ozil and it was hard to find a place for both of us in the team."