Liverpool's Jordon Ibe
The Sun suggests that the Reds are considering the offer after the 20-year-old struggled to establish himself as a key member of Jurgen Klopp's squad last season.
Liverpool manager Jurgen Klopp
However, The Sun adds that West Brom are also interested in the England under-21 international, who moved to Anfield from Wycombe Wanderers four years ago.
News of the offer from the Cherries is likely to split supporters on Merseyside. While Ibe is undoubtedly a huge prospect, who arguably has the potential to command an even higher fee in the future, he is still some way off being the finished article.
And with Klopp's reluctance to use him regularly - Ibe made 27 appearances in the Premier League last season, but started just 12 times - there may be concerns about whether they will be able to attract such an offer for him if he endures another season on the fringes of the team.
However, they will know that if they let him go this summer, he is likely to be a integral member of Eddie Howe's side, and may arrive on the south coast looking to prove a point to Klopp that he deserved more opportunities at Liverpool.
Bournemouth manager Eddie Howe