The highly-rated 21-year-old, who currently plays for ENPPI in his homeland, was linked with a move to England in the January transfer window but nothing materialised.
The Black Cats could now be about to step up their efforts to bring in Al-Muhammadi as Steve Bruce aims to bolster his attacking options.
"Al-Muhammadi had a successful trial with Sunderland at the weekend and manager Steve Bruce was impressed," agent Nader Shawki told Modern Sport TV.
"Negotiations between Sunderland and ENPPI should be concluded in the next few days."
Shawki is also the agent of Amr Zaki and is understood to have established a good relationship with Bruce during the striker's spell with Wigan last season.