Sam Allardyce has been a long-term fan of the 26-year-old Swedish international since their time together at Blackburn Rovers.
Since taking charge at West Ham, he has tried and failed to sign Olsson on a number of occasions, and now following Norwich's relegation to the Premier League he is thought to be back in for him.
West Ham are understood to have made an opening offer for Olsson but that has been rejected by Norwich - who are in no hurry to sell.
A number of other clubs, including West Brom, are also looking closely at Olsson.
Last season Allardyce used Razvan Rat, Pablo Amero, Matt Taylor and George McCartney at left-back but none of those are now at Upton Park, as West Ham look to rebuild ahead of next season.
Should they fail to land Olsson, West Ham do have other options with Dundee United's Andrew Robertson also a target along with Boca Juniors Emanuel Insua - the brother of former Liverpool defender Emiliano - and Ipswich's Aaron Cresswell.
Sky Sports understands one player who West Ham are no longer pursuing is Nice's Timothee Kolodziejczak.