West Ham are set to sign Joe Hart, which means that Randolph has been deemed expendable.
The Republic of Ireland international played a sizeable chunk of the season in goal for West Ham last term, but faced competition from Adrian.
And it seems that Bilic wants to head into the new campaign with Hart and Adrian competing for a place between the sticks.
With Newcastle looking to add a new stopper, West Ham feel that Randolph may fit well at St. James’ Park.
And Bilic reportedly plans to offer Newcastle the chance to sign Randolph, once Hart’s deal goes through.
The England international is expected to make a move to the London Stadium at the weekend.
Newcastle had actually been interested in signing Hart earlier on in the summer, but West Ham have won the race.
It is not yet clear whether Benitez will take West Ham up on their offer to allow him the chance to sign Randolph.