The Star claim the Hammers are ready to make Austin their top transfer target as new boss Slaven Bilic prepares his squad for the upcoming season.
Charlie Austin Player Profile
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And newly-promoted Bournemouth are also in the mix for the forward, who is valued at £15m.
Newcastle, Aston Villa, Tottenham and Chelsea are all known suitors of 26-year-old Austin - with the latter thought to be particularly keen on landing him to boost their homegrown numbers.
But it is claimed Bournemouth may have the upper hand in negotiations because manager Eddie Howe coached the striker while at Burnley.