Scotland boss Alex McLeish has played down talk of a move to the Premiership.
Eck is an early favourite to replace Steve Bruce - his arrival could convince Eric Black, a former Aberdeen teammate, to also stay at St Andrews.
McLeish said: "I don't think this is the time to talk about that. I'm gutted for my staff and my players right now and, as I said, I remain committed to Scotland.
"We move on right away. We have a B game against the Republic of Ireland at Airdrie on Tuesday night and we took that game because we are looking to the future as well.
"The players deserve a break from senior internationals and they will just have to go at it with all guns blazing again when they come back."