The 25-year-old has yet to convince the Anfield hierarchy since his £29.5M switch from Bayer Leverkusen last summer as he fails to compete with Ronaldo Araujo at right back.
Frimpong arrived with a reputation as an explosive wing-back, but adapting to Liverpool's fast paced system and the demands of the Premier League has not been straightforward.
The Dutchman was particularly effective as a wing-back at Leverkusen, but defensive frailties have been exposed on Merseyside as Andoni Iraola looks at other options at the back.
After being dropped to the bench after just three league matches, Frimpong is struggling to get off the bench as Iraola prefers not only Araujo, but also Dominik Szoboszlai in that position.
Now, Winwin reports the defender would welcome a new experience in the Saudi Pro League and that Al Hilal has already received an offer to sign him.
Frimpong would join compatriot Crysencio Summerville as well as England and former Aston Villa striker Ollie Watkins and former Arsenal and Brazil international Gabriel Martinelli.
The defender is fit and ready for the visit to Crystal Palace on Sunday, but Araujo is likely to start ahead of him once more as Frimpong is pushed out the side ahead of the January window.