The 24-year-old enjoyed another prolific campaign under the tutelage of Xabi Alonso last term, registering 14 goals and 11 assists in 48 games across all tournaments.
Arsenal and Newcastle United have previously been strongly linked with a move for Diaby, while Manchester United have also been tipped to join the race for the France international.
However, L'Equipe - via Get French Football News - now claims that Villa are also contenders for Diaby's signature, and Unai Emery's side have now submitted their opening bid.
Diaby is believed to be attracted by the prospect of playing in the Premier League, but Villa's lack of Champions League football could hinder their chances of pulling off a deal.
The former Paris Saint-Germain youngster remains contracted to Leverkusen until 2025, but he will supposedly be allowed to depart for a reasonable offer this summer.
In terms of players potentially leaving the West Midlands, Wolverhampton Wanderers striker Raul Jimenez is reportedly attracting interest from Turkish side Adana Demirspor.
The Mexico international was a peripheral figure under Julen Lopetegui last term and failed to score a single Premier League goal in 15 top-flight appearances.
Despite Wolves' struggles in front of goal, Jimenez started just eight league games for the Molineux outfit, and both player and club are believed to be keen on a parting of the ways this summer.
According to Turkish outlet Aksam Spor - via AS - Adana Demirspor have shown an interest in acquiring Jimenez's services, and the striker recently met with head coach Patrick Kluivert.
The report adds that negotiations are expected to accelerate in the coming days, as Jimenez prepares to leave Wolves following a successful five-year stay in the West Midlands.
The 32-year-old has amassed 57 goals and 24 assists in 166 matches for Wolves since initially joining on loan from Benfica in 2018, but he is due to become a free agent next year.
Meanwhile, former Cardiff City youngster Aaron Ramsey is apparently set to snub a lucrative move to Saudi Arabia in order to return to his boyhood club.
The 32-year-old ended his injury-hit spell at Juventus last term to join French outfit Nice, providing one goal and three assists in 34 matches for Les Aiglons across all competitions.
Ramsey's contract at Nice is due to run until the end of next season, as he automatically triggered a one-year extension by playing a certain number of games in the 2022-23 season, but he has been linked with a switch to the Middle East.
However, The Sun claims that Ramsey will turn down a mammoth payday in the Saudi Pro League in order to rejoin Cardiff, whom he represented for nine years between 1999 and 2008.
Nice are expecting Ramsey back for pre-season training next week, but the report adds that he is in talks to terminate his contract with Les Aiglons in order to return to his homeland.
The Wales international played 28 times for Cardiff's first team during his initial spell, scoring three goals and providing three assists before earning a move to Arsenal.
Finally, Manchester United youngster Will Fish has supposedly agreed to return to Scottish outfit Hibernian on loan for the 2023-24 campaign.
The 20-year-old centre-back spent the 2022-23 season at Easter Road Stadium, where he contributed three goals from 21 appearances in the Scottish Premiership.
Fish has since returned to Carrington and was named in the Man United squad for their recent friendly win over Leeds in Oslo, coming on as a second-half substitute for Lisandro Martinez.
However, the Manchester Evening News states that Fish is now poised to head back to Hibs for the 2023-24 campaign, and he will snub interest from the Championship and League One to return to Scotland.
Man United will travel to Edinburgh to face French giants Lyon in a pre-season friendly next week - a convenient trip for Fish, who will apparently remain in Scotland after that game to finalise his loan move.
Fish made his debut for Man United as a late substitute on the final day of the 2020-21 Premier League season against Wolverhampton Wanderers, and he has also been loaned out to Stockport County during the early stages of his career.