Barnsley director Don Rowing said: "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.
"As always with these type of negotiations, it's a two-way thing. Mark has got to speak to his club, he is still in a job.
"But we agreed with Rotherham to have those provisional chats - and those talks have gone really well.
"The job has got to be right for him (Mark]. There's still a lot of talking still to do yet, but it's unlikely anything else will happen before the weekend. Rowing also added that it would be wrong of the club to rule out any other managers at this stage in proceedings.
"If things did fall through then it wouldn't have been fair on any other applicants, but we won't be interviewing any other candidates at this stage,"
Barnsley Chairman Patrick Cryne is due to return from holiday tomorrow to continue further discussions, meanwhile Robins himself last night added: "Barnsley sought permission to speak to me and I was given permission to speak to them and I've simply taken that opportunity.
"Nothing has been done and a decision hasn''t been made. I am the manager at Rotherham United and will be there in the morning."
The Millers face Chesterfield this Saturday, seemingly with the prospect of Robins still being in charge.