Manchester United are also said to be interested in Semenyo, who is valued at approximately £75 million by Bournemouth.
Semenyo signed a new five-year contract with Bournemouth in July, which reportedly includes a buyout clause, although the exact figure is not publicly known.
Liverpool have a pre-existing relationship with Bournemouth, having made a transfer deal for fullback Milos Kerkez over the summer.
The club's sporting director, Richard Hughes, also has a connection to Bournemouth, having previously worked at the club.