The controversial Olympiakos owner's attempt to buy Forest from Fawaz Al Hasawi is being assessed by the English Football League Executive.
Fawaz has described the deal as "99% complete". while Warburton hopes events will "reach a conclusion quickly".
"I've been very impressed by what I've heard." he told BBC Nottingham.
"It is important to know for supporters that any owners will be restricted by Financial Fair Play. That affects every single club.
"It is important this club goes forward on solid foundations, however I think the aspirations going forward will be aggressive. They know where the club needs to be, they know the history of the club and what they want to achieve."
Warburton, who was appointed as Forest manager in March, guided the Reds to Championship safety on the last day of the season.
The 54-year-old said finalising the takeover as soon as possible will be good for everyone, but there would not be a sudden flurry of transfer activity because of the need to comply with FFP regulations.
"We know where we are and the processes are taking place - and have to take place - for such a situation," Warburton added.
"Supporters naturally get excited at this time of year with a new season ahead and who are we going to buy, but FFP are in place of for a variety for reasons and we we have to adhere to them."
Evangelos Marinakis' expected takeover of Nottingham Forest will bring an 'aggressive' approach to achieving the club's goals, says boss Mark Warburton.