The 20-year-old has been regularly linked with Real Madrid while the midfielder admitted last month he would at some point in his career like to return to Barcelona, where he learned his trade before joining Arsenal in 2003.
Fabregas signed an eight-year contract with the Gunners last summer but the north London club's immediate fortunes are unsettled after the departure of striker Thierry Henry to Barcelona and continuing uncertainty over the future of manager Arsene Wenger.
However, Fabregas is adamant he will remain in north London.
He told The Sun: "In 10 days I'll be back training with Arsenal. My team. I'm staying in London."