The Yorkshire giants have been without a manager since Sam Allardyce departed Elland Road after the end of the season.
A takeover by minority owners the 49ers has delayed matters, but Leeds are now closing in on announcing their new boss.
Former Crystal Palace boss Vieira was keen on the role and held interviews with Leeds about taking charge.
And it is claimed that the Frenchman performed strongly in the talks with Leeds.
Despite that, Leeds are set to go with ex-Norwich City manager Farke, who has experience of guiding a side out of the Championship.
With Leeds awaiting ratification of their takeover from the EFL, the jury is out on exactly when Farke will be confirmed as the club’s new boss.
The clock is ticking down though with pre-season training looming for Leeds and then friendly fixtures for the side to get stuck into.