German playmaker Ozil is about to enter the final year of his Gunners contract and has struggled to make much of an impact this term.
Campbell, who spent seven seasons in Arsenal's first team during his playing days, believes that Aston Villa star Grealish and Leicester City midfielder Maddison are the type of player Mikel Arteta should be looking at.
"Arsenal need an all-rounder in midfield, someone in the middle of the pitch who not only can create, but can break the play up, has got legs, we miss that," he told Metro. "We've been a strong spine for years. There was talk of should we go for Jack Grealish or James Maddison, these types of guys would improve Arsenal.
"No disrespect to Mesut Ozil, but Ozil is on the wrong side of his Arsenal career with a year left on his contract after this. But we need someone who's going to be in there with legs, we need creativity, and someone that when the game's not going particularly well, he can get stuck in and knuckle down as well.
"We're being shown up by the likes of Sheffield United. Chris Wilder who has done a fantastic job there, they haven't got the quality that Arsenal have but they're above us in the league.
"Why? Because they've got a system and they fight, grab and battle, and they've got some quality there as well. If we can't match these teams, we don't deserve to be up there."
Grealish has seven goals and six assists in 26 Premier League appearances for Villa this term, compared to six and three respectively for Leicester midfielder Maddison in 28 outings.