Now 36 years of age, the Czech custodian has spent the last three seasons at Emirates Stadium.
He still has a year left to run on his current contract and has no intention of breaking that agreement, despite Arsenal having invested €22 million (£19m/$26m) in Germany international Bernd Leno.
Cech intends to remain in north London and battle the new boy for starting duties under Unai Emery, with any interest from afar being shunned at this stage.
“My contract with Arsenal still has a year to run,” Cech told journalists in Zruc during a visit to his homeland.
“The only thing I’m preparing for is the fight for the No. 1 spot in goal.
“Napoli were interested but my future is at Arsenal. I didn’t think of changing clubs.”
It had been suggested that Napoli were eager to take Cech from the Gunners on a season-long loan.
Cech has forced them to look elsewhere, but there could still be movement on the keeping front at the Emirates.
With Leno on board and Cech staying put, David Ospina is facing up to being third choice.
The Colombia international has already hinted that he could be on the move during the summer transfer window, with his options set to be explored once World Cup duty comes to a close.
Fenerbahce have been linked with the 29-year-old, with the Turkish giants also among those reported to be keen on taking Jack Wilshere as a free agent following the expiration of his contract at Arsenal.