Basescu spoke during a news conference in Slovakia's capital, Bratislava.
Basescu, who is on an official visit to Slovakia, made no other comment on the subject.
His Slovak counterpart, Ivan Gasparovic, also said he had "received no request," echoing the comments of several Slovak ministers last week. Gasparovic added that Slovakia "would not accept anything of this nature" on Slovak territory.
"The Washington Post" daily said last week that the CIA was holding Al-Qaeda terrorist suspects in secret prisons in eastern Europe and elsewhere.
The U.S.-based rights group Human Rights Watch said it is "practically convinced" that such installations exist, "at least in Poland and Romania."