Ukraine is set to jointly host Euro 2012 with Poland.
"If this city [Kiev] is late with the construction of the stadium, then Euro 2012 will take place exclusively in Poland," Platini was quoted as saying by the Dziennik paper.
He also denied earlier rumors that Germany could replace Ukraine as joint hosts.
Ukrainian efforts to prepare for Euro 2012, already behind schedule, have been further hit by the global financial crisis.
This is not the first time that UEFA has expressed its dissatisfaction with Kiev's preparations for the tournament.
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