This is according to the former player of the Premier League Tony Cascarino.
Ramsey is leaving North London in the summer to play for Juventus, where he signed a four and a half year contract.
Ramsey, however, was one of the Arsenal's most productive players this season, and many supporters believe the club has to sign a replacement.
The Gunners have been connected with the likes of Yannick Carrasco, Aaron Wan-Bissaka and Samuel Umtiti, but no one can fill the void that Ramsey will leave.
But Cascarino, who has played for more teams including Chelsea and Celtic during his career as a player, believes that the Arsenal should sign one of the men of the Leicester stars.
"I look at Maddison and I think," Arsenal is your team, "he told the Times.
"There are not many great No.10s in the world of football, but the Arsenal is in desperate need of someone to play as the man of Leicester City.
"The role was considered a luxury in the past, their job was to create opportunities and make a difference in attack."
Cascarino also stated that it is difficult for The Maddison players to be defended and "work hard", but it was something in which the number 10 was improving.
"Mesut Ozil and Dele Alli should deliver without the ball and act as a defender for their teams," he added.
"You have to be very gifted to do it and nine out of ten players don't want to work without the ball.
"Maddison's work rate is good and is improving.
"No doubt it is technical enough for maximum flight."
Maddison just signed for Leicester last summer from Norwich, but he was one of the most impressive players this season.
He has scored seven goals and registered six assists for the foxes this season and is one of the most effective free-kickers in the league.