Scotland international Maloney is expected to complete a move from Hull but Aberdeen's attempts to sign former St Johnstone striker May have been hit by Simon Grayson's decision to leave Preston to take over as Sunderland manager.
McInnes has until Friday night to register his Europa League squad although he could add one more player before Aberdeen face Kazakhstan's Ordabasy or Bosnians Siroki Brijeg at Pittodrie on July 13.
Quoted on Aberdeen's official website, McInnes said: "Out of respect to Shaun Maloney and Hull City I don't want to say too much
Hopefully there might be an announcement next week
I am confident but we have been here before
Until someone actually signs and all the paperwork is complete I don't like saying anything
"He is the type of player in terms of level of ability we want and a player who can handle the demands of our club and that is important."
On May, the former St Johnstone boss said: "Again I don't want to speak too much about it
My high regard for him is well known but he is Preston's player
He is someone we have had conversations about with Preston but he is their player and it is their call
Obviously they have a manager to appoint."
McInnes, whose side beat St Johnstone 3-0 in a McDiarmid Park friendly on Saturday, added: "We probably have another three or four signings to make
We would like to bring in another centre-forward
We would like a wide player - you could see we were playing with no real width because young Scott Wright was injured
We would have liked to have started him but he has been feeling his hamstring a little bit so we did not take a risk
"We have work to do and we have targets we have been looking at
We are working hard to try and bring them in
Whether we can get them in before the European deadline remains to be seen
It is more important we get the right ones in regardless of the deadline."
Aberdeen have German defender Berkay Dabanli on trial but McInnes revealed former Dons full-back Kevin McNaughton was only with them to keep his fitness up after leaving Inverness.
Source : PA
Source: PA