The 24-year-old has enjoyed a hugely-impressive four years at the Bundesliga outfit, contributing 49 goals and 48 assists from 172 appearances in all competitions.
At a time when Xabi Alonso is attempting to get Leverkusen back into the Champions League, the France international could theoretically remain as a key player.
However, Leverkusen are allegedly open to doing business for the right price, fellow admirers Aston Villa yet to meet that mark in negotiations.
The Premier League outfit have reportedly failed with a bid in the region of £30m, Leverkusen instead ready to push to recoup £50m.
With Unai Emery regarding Diaby as a key target ahead of Villa's return to European football, a fresh approach is expected to be made in due course.
Nevertheless, according to the Daily Mail, failure to quickly wrap up a deal has left Villa vulnerable to interest from Saudi Arabia.
The report suggests that Al-Nassr are looking to secure the signature of Diaby at a time when they are eager to make up for lost time in the transfer market.
Over the weekend, it became apparent that FIFA had lifted the ban that had been imposed on Al-Nassr due to their failure to make an arranged payment to Leicester City for Ahmed Musa.
Al-Nassr, who have Cristiano Ronaldo in their squad, have purchased Inter Milan midfielder Marcelo Brozovic in recent weeks, yet they have been the least active of the four teams owned by the Public Investment Fund.
Chelsea winger Hakim Ziyech had been on course to sign for Al-Nassr before the transfer was scrapped due to an issue with the Morocco international's medical.
Diaby has now seemingly been identified as the like-for-like alternative, even though he will cost considerably more than Ziyech if a deal goes through.
As it stands, it is unclear whether other clubs will re-enter the race for Diaby, who has two years left on his contract with Leverkusen.