Blackburn Rovers are chasing AS Monaco striker Eidur Gudjohnsen.
The News of the World says Gudjohnsen, 31, was close to linking up with former team-mate Gianfranco Zola at West Ham last summer but instead opted for a spell in France.
Allardyce set the ex-Chelsea and Barcelona star on the path to fame when they worked together at Bolton 10 years ago.
He helped the Blues win two successive Premier League titles before earning a move to the Nou Camp in 2006.