The Hammers started the season superbly, but having won just once in the last 12 games, the pressure is once again on manager Sam Allardyce.
The 60-year-old is out of contract this summer, and currently looks unlikely to be offered a new one, with West Ham possibly looking to be more ambitious with their next appointment.
The Daily Mirror report that Bournemouth boss Howe is on West Ham's list of candidates to replace Allardyce, with members of the Upton Park hierarchy impressed with what he's achieved at Bournemouth.
Howe, 37, is one of the Football League's youngest managers - and despite his youth, the Cherries are vying for automatic promotion to the Premier League, less than two years since Howe guided them to promotion from League One.
Howe is one of the brightest up-and-coming managers in England, and the Mirror also suggest that West Ham aren't alone in considering him as their new manager.
They also report that Sunderland have Howe as their top target when Dick Advocaat's short-term contract expires at the end of the season, which could spark a real battle for his services - especially if Bournemouth miss out on promotion this season.