The Ligue 1 giants are open to selling the French talent for a suitable offer amid growing interest in the player.
With a contract running until June 2028, Monaco value Akliouche at around €60 million.
Leverkusen have identified Akliouche as their dream target to bolster the attack, but the deal is still in its infancy.
Nottingham Forest, Tottenham Hotspur and Barcelona have also been credited as the suitors for the 23-year-old.
A standout youth product of Monaco, Akliouche has grown by leaps and bounds as one of the top young talents in the French top flight.
He had a productive 2024/25 campaign, registering seven goals and 12 assists in all competitions.
Akliouche also bagged a silver medal with France in the Paris Olympics last year.
The French-Algerian youngster ranks among the prominent wingers in Europe, excelling in ball progression, dribbling and playmaking.
Leverkusen are looking to strengthen their squad with quality signings on all fronts, as they aim to compete for more trophies under new manager Erik ten Hag.
They will have significant spending power, having sold Florian Wirtz and Jeremie Frimpong to Liverpool for around €170 million.
Leverkusen can be a great destination for Akliouche to reach new heights in his career. He would bring more dynamism to their attack.
The German giants have secured a deal worth £35m for the signing of Liverpool centre-back Jarell Quansah.
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