The 24-year-old joined the Rams in March from Norwich City on a loan deal until the end of the season.
His contract is due to expire in June and when asked by the Derby Telegraph regarding his thoughts over a free transfer to Pride Park, the striker replied: "Yes, I'd definitely be open to it. I can't really focus too much on it while the season is going on but I'll be looking to finish strongly and see where that takes me. The fans have been great and the lads as well."
Martin came through the ranks at Norwich, having joined the Canaries as a trainee back in 1998.