The Sunday Mirror says Pearson has emerged as one of the shock front-runners to replace Gianfranco Zola at West Ham.
The Hammers will part company with the Italian at the end of the campaign regardless of whether he steers the club to safety.
Co-owners David Sullivan and David Gold have begun to consider their options and Leicester boss Pearson is figuring high on their wish list.
He could even steer Leicester to successive promotions after virtually assuring the Midlands club of a play-off place this season.
But Pearson, who is one of the lowest paid managers in the Championship, has refused to commit himself to Leicester beyond the final year of his current contract.
It would effectively cost West Ham as little as £350,00 to prize him away from the Walkers Stadium as compensation in his deal is restricted to just one year of his current salary.