West Ham are desperate to land a new left-back, following an injury that Aaron Cresswell picked up over pre-season.
Cresswell is set to miss the opening few months of the campaign, leaving Slaven Bilic’s options short on the left hand side of his defence.
West Ham have been linked with a host of targets - including Manchester United’s Cameron Borthwick-Jackson and Arsenal’s Kieran Gibbs.
However, they seem to have made Olsson their top target, and a deal could go through soon.
Norwich have already rejected a £3 million bid for Olsson, but the Mail suggest a repeat offer could be made.
West Ham are said to be willing to pay £5 million for the Swedish international, which could be enough to persuade Norwich to sell up.
West Ham start their Premier League campaign in two weeks’ time, with a match against Chelsea at Stamford Bridge.