According to the Liverpool Echo, the Reds continue to search for a new attacking option and has identified the 23-year-old as a potential signing.
The Merseyside giants have a strong relationship with the Bundesliga outfit, having previously acquired players including Sadio Mane, Naby Keita, Takumi Minamino and also the most recent addition Ibrahima Konate.
The 22-year-old was heavily linked with a move away from the East London outfit throughout the summer, but remained with the Hammers.
90min reports that Rice expects this campaign to be his last in the London Stadium, amid interest from Manchester City, Manchester United and Chelsea.
The 24-year-old joined the Cherries in 2019, but with the club failing to secure promotion back to the top flight, the attacker is now considering a transfer.
According to Marca, the Dutchman’s performances last season have understandably attracted interest from other top European clubs including Liverpool.