Dowie has guided Crystal Palace to a possible Division One play-off place and his good work at Selhurst Park has led to speculation that potential new Whites owner Parkin would bring him to Elland Road to replace Gray.
Parkin is thought to have tabled an improved £30m bid for the club.
Gray is due to discuss his future at another board meeting with Richmond and Leeds chairman Gerald Krasner next week.
However, Leeds director Melvyn Helme told the Yorkshire Evening Post: "If someone else wants to appoint the manager of this football club they should be in control because as far as we are concerned we have a manager."