Sydney is set to keep John Longmire, with the premiership-winning coach to reject an offer from North Melbourne in order to stay at the Swans.

According to the Herald Sun, Longmire is "almost certain" to sign a new contract with the Swans, which would be added on to his current contract that takes him through to the end of the 2020 season.

Longmire won a flag in his second season with the Swans in 2012, and has a 65.4% winning record with Sydney.

The Roos' pursuit of Longmire looks to have come to an end, meaning current caretaker coach Rhyce Shaw is in the box seat for the permanent role.

North Melbourne has won four of their five games under Shaw, including wins over Richmond and Collingwood.