The 29-year-old Campbell is reported to have attracted Premier League interest following the Seasiders' relegation out of the top flight last season.
Sunderland were reported to be leading the chase early on, while Aston Villa have also been linked with an approach.
Campbell plundered 13 goals in the top flight last season, proving he has what it takes to compete among England's elite.
He could, however, be tempted to remain in the second tier and join West Ham's promotion push.
The Hammers are looking to bounce back into the top flight at the first time of asking and Sam Allardyce is busy piecing together a squad capable of taking that step.
It is understood that he is keen to bring Campbell on board and discussions regarding a possible deal have begun.
Striker Cole is expected to join Stoke City this week after the Hammers accepted a bid from the Potters for him.