Congerton is understood to have made it known to club owner Ellis Short last week that he would looking to end his 18-month stay with the club – with HITC Sport bringing you that news prior to the latest round of Premier League fixtures.
However, Short and Sunderland already knew that Dick Advocaat would be leaving after their match with West Ham United, which the club confirmed on Sunday.
Now Congerton could be tasked with helping to find Advocaat's replacement, although HITC Sport has been told that an appointment this week is unlikely.
Former Sunderland defender and ex-Newcastle United boss Sam Allardyce remains favourite for the role, although Burnley boss Sean Dyche and former Leicester City chief Nigel Pearson are also under consideration.
It is all change once again at the Stadium of Light, but it may be some time before Congerton is given the opportunity to add his name to the departed list.