Allegedly the club have "grown tired" of Simpson’s protracted contract negotiations and will allow him to depart in the close season if their valuation of the right-back is met.
And Best will also be made available for transfer.
The striker has grown frustrated since the serious ankle injury he picked up in early February.
Both have been part of the squad since the Championship promotion season, but United illustrated last summer that they are prepared to be ruthless in their bid to keep progressing.
Simpson insists he wants to stay at Newcastle but is understood to be looking for better terms than the £25,000-a-week final offer that United have tabled to him.
Newcastle were involved in negotiations with Celtic on transfer deadline day over Best and would be open to offers for the forward again this summer.
Fraser Forster is wanted by Celtic in a transfer likely to generate transfer funds for Pardew, but the player is holding out for a bigger offer from a club in the Premiership.
Danny Guthrie’s future is also up in the air, with the midfielder understood to have rejected a contract offer tabled by United.