Senior members of the Conservative-controlled Norfolk council are refusing to confirm Mr Bryant's status following reports that the council was ready to offer him a package totalling£270,000. This figure is understood to include his pension contributions.
As LGC went to press Mr Bryant remained away from work, despite the maximum two month suspension period for a chief executive ending last week.
Under their conditions of service no chief executive is supposed to be suspended for any longer than two months unless an independent investigation has found good reason to extend the suspension.
Mr Bryant, who could not be reached for comment, was suspended in February after the Labour Party resumed judicial review proceedings over the treatment of its group leader, Barbara Lashley. Mr Bryant restricted Ms Lashley's access to council buildings because of her alleged manner towards staff.
He lifted the restrictions after the party sought a judicial review of the decision, but the council's standards committee later found her behaviour had fallen short of the required standard.