Terry was axed as England captain on Friday with the defender due to stand trial for racially abusing QPR defender Anton Ferdinand. Terry has pleaded not guilty to the charges.
England manager Fabio Capello spoke out against the FA board's decision to intervene, claiming he "strongly disagreed" with the move to strip Terry of the armband.
But while Gerrard has struggled with injury problems and the midfielders are not guaranteed to start, Hart's status as England's No. 1 means he is an automatic choice. However, despite being flattered to be linked with the vacancy, he insists he is not thinking about captaincy.
"I am flattered to be linked with it but anyone who's having a consistent run in the England side is being linked with it," Hart said. "There are a lot stronger candidates than me. I don't have a view on who should be captain. As long as I'm playing I don't care.
"I have got a really important season with games for Manchester City and hopefully a couple for England coming up. That is all I am concentrating on at the moment."