Bournemouth have been impressed by Clyne during his loan spell this year and want to make the deal permanent.
However, the Hammers have also taken a liking to Clyne and are preparing to battle the Cherries for his signature, according to Goal.com.
Liverpool will reportedly hope to make a slight profit on Clyne by asking for around £15m – £2.5m more than they signed him for from Southampton in July 2015.
It's believed that Clyne, 28, has formed a good relationship with Bournemouth manager Eddie Howe, and is enjoying his time on the south coast.
But West Ham are a London club and Clyne himself is from Stockwell, so a move back to the big smoke isn't out of the question.
READ MORE...
QUIZ! Can you name the 35 Liverpool players with 20+ Champions League appearances?
LIST The 15 best players ever to be relegated from the Premier League
Manchester United eyeing surprise move for AC Milan star for whom tension in Italy is growing: report
‘Even though Kevin Keegan was my boyhood hero, we never really saw eye-to-eye. That was an underwhelming time for me – I felt on the outside’: Newcastle cult hero reveals disappointment over how things went under King Kev
