The Gills gained promotion to League One earlier this month, but rather than settle for a campaign of securing survival, Allen has insisted that his players should aim to emulate the likes of Norwich City and Southampton.
"I need some time now to get the team together and build for next season," he told the club's official website. "I want to challenge and make it good for our supporters and players.
"We want to continue the roll we are on. Norwich and Southampton went from League One to the Premier League and I don't think we should set our vision for the future any lower."
Allen took charge at the Priestfield Stadium last July.