A move for Docherty appeared to have stalled earlier this week, with interest from Charlton, but Parkinson says the deal is not fully dead and the Black Cats will reassess their midfield options over the coming days.
Speaking ahead of the visit of Doncaster Rovers to the Stadium of Light, Parkinson also confirmed the club has made an enquiry about Ollie Norburn at Shrewsbury but again stressed he was just one possible option the club is considering.
Central midfield is one area Parkinson is aiming to strengthen ahead of the January 31 deadline.
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On Docherty, Parkinson said: “Greg is one of a number of players we are looking at in that position, we have made contact with Rangers.
“We are weighing up all of our options.
“We will sit down after the weekend and see where we want to go. Greg has other options as well.”
Pressed on whether the deal was dead, Parkinson added: “It is not completely dead.
“At this stage there are many players we have spoken to, club and agents wise, some names come out, some don’t. Greg is one of those.”
On Norburn, Parkinson added: “Another player we had watched and looked at, we made an enquiry about him.
“Honestly, it is just a number of situations we are weighing up and working on.”
And does Parkinson think Sunderland’s transfer business will go to the wire?
He added: “We only really want to get players in who will improve us, not just bring in for the sake of it.
“Will it go to the wire? Normally for one reason or another the last day is busy.
“It is because other clubs are waiting to get players in, it is a domino effect, so it could well do if we bring anyone in.”
The deadline is 11pm on Friday, January 31.