As reported by The Metro, the Colombian international told reporters he supported Arsenal growing up as child and is full of admiration for club's philosophy under Arsene Wenger.
Chelsea boss Jose Mourinho said earlier this week that his club are not interested in signing another striker this month, while Arsenal are expected to strengthen with Nicklas Bendtner sidelined.
The Danish international is the Gunners' only back-up striker so Martinez's transfer hint could alert Wenger to his availability.
Martinez said: "I cheered for Arsenal when I was a kid - I love their style of play.
"It's flowing and open with a lot of first touch passes. It would be suitable for a player like me. If I get a chance to play for a high level club like Arsenal I wouldn't hesitate to accept it."
The Porto ace has been stalling on a new contract, and the report claims the £30m-rated striker is all but set to leave the club - either in the next few weeks or this upcoming summer.
Both Chelsea and Arsenal are well-placed to mount a Premier League title challenge over the course of the second half of the season.
And the January transfer window could be crucial in deciding what is shaping up to be an extremely tight title race.
Chelsea were linked with a move for Martinez in late November after Mourinho reportedly became frustrated with his goal-shy striker trio of Fernando Torres, Demba Ba and Samuel Eto'o.