The Hammers snapped up midfielders Pedro Obiang and Alex Song over the summer, but are now being linked with a further move to strengthen their options.
With Song only on a season-long loan from Barcelona, Slaven Bilic's men could at least consider other options for a permanent deal, and The Sun suggest that Dan Gosling is one potential target.
The 25-year-old midfielder, formerly of Plymouth Argyle, Everton and Newcastle United, has enjoyed a strong start to the Premier League season with Bournemouth, even if the Cherries have struggled with the step-up to the top flight this season.
Gosling has had his career littered with injuries, but is currently fully fit - and is earning a reputation for his fitness having been all over the park for Bournemouth so far this term.
Now, it appears that West Ham are interested in exploring a deal for Gosling, in case they pursue an alternative permanent option to Song.
The midfielder wouldn't be a big name signing for West Ham, and his recent injury problems are something that certainly need exploring if Bilic does pursue a deal, but he could provide solid competition for places in the heart of the Hammers' midfield.