Martins, 22, told The Sun: "Flattered? Well, maybe, you must be doing something nice to be linked with a club like Arsenal.
"If it's true, I must say it was a good thing to have interested a club like Arsenal. But I have a club, which I am happy about. I am committed to the Newcastle cause.
"I am employed by Newcastle and I owe them my dedication and that is it."
Despite competition from Michael Owen and Mark Viduka, Martins wants to sign a new long-term deal on Tyneside.
He added: "I am ready to fight for a place."