West Ham are desperate to add a new left-back, following an injury to Aaron Cresswell.
Cresswell is set to miss the first four months of the season, in what is a major blow to Slaven Bilic’s side.
While Sam Byram has played at left-back over pre-season, the former Leeds United defender is more comfortable in the right hand side of defence - and it is thought that Bilic wants to bring in a specialist before the season starts.
West Ham have been linked with both Arsenal’s Kieran Gibbs and Manchester United’s Cameron Borthwick-Jackson, but Olsson appears to be another on their wishlist.
Olsson impressed for Norwich last term, despite their relegation, with his attacking qualities shining through.
Norwich are determined to keep hold of the Swedish international and they have rejected the Hammers’ first offer.
It remains to be seen whether West Ham will now come back with a repeat bid, or move on to other targets.