Gallagher has been named in every England squad since the 2022 World Cup, where he was an unused substitute, having made five appearances in Euro qualifying games.
The 24-year-old, who has been with Chelsea since the age of six, has captained the Premier League club on several occasions this season while Reece James and Ben Chilwell were sidelined by injury.
Gallagher has been one of the few dependable players for Chelsea in a season where Mauricio Pochettino's squad has struggled for consistency, having made 38 appearances across all competitions.
"I've had to step up and be more of a leader this season at Chelsea which I've really enjoyed and I think that's helped me develop more as a player as well," Gallagher told reporters after England's 1-0 defeat to Brazil in an international friendly on Saturday.
His 90th-minute winner against Leeds United last month helped Chelsea advance to the FA Cup quarter-finals, where they beat Leicester City to set up a semi-final clash against Manchester City.
"The experience I've had in the two cup competitions with Chelsea and getting as far as we have done will definitely help being in those positions," he said.
"It is what (England manager) Gareth (Southgate) and the others are looking at. I'll continue to work my hardest for Chelsea and give myself the best opportunity to be in (the Euros) squad."
England, who face Belgium on Tuesday in a friendly match, are grouped with Slovenia, Denmark and Serbia at Euro 2024, which begins on June 14th.
