Both Arthur and McDermott have been asked by Sri Lanka Cricket to travel to Pakistan with the Sri Lanka Test team later this month before officially taking over by December when their contracts will be signed.
"We are having discussions with Mickey. We think we will be able to reach an agreement," Sri Lanka Cricket (SLC) CEO Ashley de Silva told ESPNCricinfo.
"He had won the 2017 Champions Trophy with Pakistan and had also taken Pakistan to the number one spot in T20s. He's a well-known coach and he's been around for a while," he added.
SLC has been looking for a new coach ever since the end of the ICC Men's Cricket World Cup. Arthur has previously coached South Africa, Australia and Pakistan in the past.