The 37-year-old, who signed a new one-year contract this week, is likely to start the new campaign as Chris Hutchings' preferred choice ahead of the 22-year-old Dubliner, but Ince knows Gilmartin is rapidly improving.
Gilmartin was given a chance towards the end of last season when Ince was away on international duty and he performed so well that the Trinidad & Tobago star was left on the bench when he returned.
However, Gilmartin made a few costly errors in the home defeat to Huddersfield and Ince was drafted back into the side for the final games of the season.
"Rene did an excellent job while I was away and his performances helped the team," Ince told the Birmingham Mail.
"He's pushing me and I can't sit back because football isn't a game where you can sit back and watch it go by. You have to push to the best of your ability and play as long as you can."