With no incomings at Craven Cottage on Tuesday, Schwarzer remains part of Hughes' plans and he is pleased to have retained a player of his considerable ability.
He told Sky Sports News: "We talked about Mark's situation on a number of occasions and ideally we wanted him to stay. We understood that there was an interest from Arsenal but given our current goalkeeping situation there was no chance of him leaving."
Reports suggested the Gunners had made one last attempt to prise Schwarzer away with a £4million bid, but Hughes insists no such offer was received.
"No, it didn't. There were two real strong enquiries but there was never a bid today," he added.