According to The Mirror, West Ham could make a move for Arter in the January transfer window.
Arter has been on the books of Bournemouth since 2010 and is an important player for the Cherries.
The 27-year-old midfielder has proved himself in the Premier League and has been a success in the top flight of English football.
Bournemouth are just a point and a place above the Hammers and are also in danger of going down to the second tier of English football.
West Ham fans have taken to Twitter to give their reaction to speculation linking the club with a move for Bournemouth midfielder Arter.
Below are some of the best comments:
He would bring much needed energy thats for sure— Neil Thompson (@NJThompson94) November 10, 2017
OMFGGGGGG HARRY ARTER'S CLARET & BLUE ARMY https://t.co/0e9H83tnj2— Brad (@Brad_WHU) November 10, 2017
Yes Not keen on Arter either, too many like Snoddy and Jarvis at silly money....— Philip 父 Wilkinson 父 (@PW57WHU) November 10, 2017