Sky Sports sources understand West Ham are hoping to conclude the signing of West Brom defender Jonas Olsson after Euro 2012.
The centre-back, who has been representing Sweden in Group D of the tournament opposite England, France and Ukraine, is out of contract at The Hawthorns next summer.
Olsson has previously hinted he would be open to a new challenge away from the Baggies, who recently appointed Steve Clarke as their new boss.
Tottenham were reported to be chasing his signature but it is uncertain whether he is still a target following the sacking of manager Harry Redknapp.
Aston Villa, Fulham, Everton, and Turkish side Galatasaray have also been linked with the stopper but it appears the Hammers could beat them to the punch.
The 29-year-old, who joined the Baggies from NEC Nijmegen in 2008, has previously said he will make a decision on his future after the Euros.
West Ham boss Sam Allardyce is keen to strengthen his options after guiding the club back into the Premier League last season.