The Argentine international, who joined City in the summer from Manchester United, said he bumped into Henry in the carpark after Arsenal had played Tevez's former club West Ham in 2006 and the Frenchman said he should come and join him at the Gunners.
"He said, 'Hey, what are you doing here? Come and play with us - it's incredible that you can't get a game in this team'."
But Tevez said he was happy to fight for his place in the team at Upton Park at the time and has done the same at every other club he has been at.
"Having got this far in my career, fighting for my place doesn't bother me. I'm used to it. I've had it at all the big clubs I've played for," he added.
"At Boca, Corinthians, West Ham, United and City. It's normal for there to be lots of good strikers. I never let my head drop. The harder the challenge, the more effort I put in to win a place. That's what I am doing here."