Ibe, 20, has been given permission to speak to the Cherries after a 2015-16 season that saw him make 12 Premier League starts for the Reds.
The transfer would top the reported £10m Bournemouth paid Wolves for Benik Afobe in January.
England Under-21 winger Ibe has made 58 appearances for Liverpool since signing from Wycombe Wanderers in 2011.
Ibe had been earmarked as the natural replacement at Anfield for Raheem Sterling after he made a £49m move to Manchester City last summer.
The youngster's form dipped, however, and he was not a regular under Jurgen Klopp after he succeeded Brendan Rodgers as manager.
Ibe did show a glimpse of his promise with a spectacular goal at West Bromwich Albion in Liverpool's final Premier League game of last season.
Bournemouth are seeking reinforcements after selling Matt Ritchie to Newcastle United in a deal that could eventually be worth £12m.
Bournemouth have had a club record £15m offer for Liverpool winger Jordon Ibe accepted.