The Sun says John W Henry and his Fenway Sports Group are actively hunting a new manager.
The American owners will NOT, however, rush into an appointment and will only move when they have found the right man.
Marseille's Didier Deschamps and Owen Coyle - boss of today's Anfield visitors Bolton - are high on the list, but both are currently unavailable.
That could buy Hodgson a little longer, even though his long-term fate is already sealed, just six months into the job.
Ex-Barcelona boss Frank Rijkaard is out of work but not the shoo-in bookies rate him.