Nathaniel Clyne is also expected to move to the Vitality Stadium.
Bournemouth have signed Liverpool striker Dominic Solanke in a £19million deal.
The 21-year-old had attracted interest from Crystal Palace in recent weeks but after they cooled on a deal the Cherries moved in and Independent Sport understands an initial fee has been agreed, with extra payments factored in.
Solanke's arrival, likely to be the first of two moves from Anfield to the Vitality Stadium with defender Nathaniel Clyne set to join on loan until the end of the season, will pave the way for Jermain Defoe to join Rangers on an 18-month loan.
The 36-year-old former England striker has found his first-team chances limited this season.
Solanke, who moved to Anfield in the summer of May 2017 for an undisclosed compensation fee as a former academy player, and made 27 appearances in his first season but has yet to feature in the current campaign.
The 21-year-old is keen to play first-team football, having left Chelsea for exactly that same reason and with little chance of displacing the trio of Roberto Firmino, Sadio Mane or Mohamed Salah in the near future has decided to look elsewhere.
Speaking to afcbTV, Solanke said: "I think the club is going somewhere. Over the past few years, they have been really good in the Premier League and had some good positional finishes as well. I think it's a good club to be at, especially for someone of my age.
"I spoke with the manager this morning (Friday). He is a really nice guy. From playing and watching the Premier League, I know the sort of manager he is. I was excited to meet him and am really looking forward to working with him and seeing what he's about.
"My main target is to score goals and, being a striker, hopefully I can get a few for the team and help the team get wins. Playing in the Premier League, every game is tough and together we can try to do as well as we can."
Clyne is in a similar position in having seen his first-team chances drastically reduced due to the form of Trent Alexander-Arnold and Joe Gomez.
Although the latter is currently injured he is expected back from a fractured bone in his foot in the next fortnight and therefore Jurgen Klopp is prepared to allow the 27-year-old to leave even though they are in the middle of a title battle with Manchester City.
Clyne has played just five times this season and managed only a similar number in the previous campaign because of a back problem.
Gary Neville and Jamie Carragher have differing views as to who holds the balance of power in the Premier League title race after last night's thrilling encounter between Man City and Liverpool.