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.
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