The national team suffered a disappointing 3-1 defeat against Ukraine in their World Cup play-off semi-final in June, so will miss out on this year’s tournament.
Gordon impressed in the game despite it ending in disappointment and went on to win his 70th cap in the Nations League victory in Armenia.
The former Celtic and Sunderland keeper signed a new contract at Tynecastle last season which will keep him at the club until the summer of 2024, when the next European Championship finals take place in Germany.
When asked about Euro 2024 at the launch of the world’s largest inflatable assault course at Conifox Adventure Park in Edinburgh, the Hearts captain said: “I’ll just keep going as long as I can. It’s up to the manager to pick the team but I’ll try and play as well as I can for Hearts.
“If I do well there then I give myself a chance to get picked by the manager.”