The 28-year-old is a key figure at the heart of Sean Dyche's defence having played in all but two of Burnley's Premier League games last season.
Tarkowski is a former player of Brentford and it is believed that he would jump at the chance to move back to the capital, and the Hammers are reportedly ready to pursue a deal.
Football Insider reports that West Ham put in a series of bids that rose to £30m for the centre-back last year but Burnley held firm to retain their centre-back.
However, Tarkowski only has one year remaining on his contract at Turf Moor and the Clarets will not want to risk losing him on a free transfer next summer, so could cash in on him in the coming months.
Tarkowski arrived at Burnley in 2016 and has gone on to make 182 appearances for the club, getting six goals along the way. body check tags ::