Rotherham boss Robins held provisional talks with Rowing and fellow Tykes director Barry Taylor on Wednesday night.
Rowing said talks between the two parties went "really well" in the two-hour meeting.
"We've had provisional talks with Mark - and those talks have gone really well," he told the Sheffield Star.
"We are still in talks at this stage, but we are looking to meet again to conclude those talks.
"I think the fact we're in talks probably indicates that Mark is a our leading contender. Mark's a promising young manager and we rate him very highly."