The 23-year-old Alonso was on loan at Sunderland last season from Serie A outfit Fiorentina.
Talks have advanced over the last few days, and West Ham has said they are prepared to make an announcement about an unnamed signing later today.
West Ham manager Sam Allardyce is looking to acquire a new left back after losing George McCartney, whose contract expired with the club.
Alonso is believed to want to leave the Italian side permanently after growing comfortable playing in the Premier League the second time around with the Black Cats.
Many believe Alonso’s price tag of £1.5million would be a bargain for the cash conscious Hammers.
Alonso performed well while at Sunderland last term, helping them reach the final of the Capital One Cup.
He played sparingly for Bolton from 2010-2013, appearing in just 46 matches with the club during that time. He came into his own in 2012, however, playing 30 matches and notching four goals for the Wanderers.