Davids' agent admitted signing for the Championship side would interest the 36-year-old, and the two parties have held talks about the possibility of a move.
But the Foxes chief has cranked up the pressure by demanding an answer from the former Ajax player.
City want a deal wrapped up in time for their trip to play-off rivals QPR on Friday.
"We have given him 24 hours to respond," Mandaric said.
"At the moment, I'm not sure where we are with it. I don't know, nor have I been given, any indication one way or other.
"I'd say it's 50-50 at the moment. By today, we should find out more."
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