A number of national newspapers in England suggested on Tuesday that PSG were lining up a summer swoop for England international Rooney.
Leonardo has distanced PSG from these deals, although the Brazilian did admit the Qatari-backed French club would be looking to strengthen before next season.
"On Ronaldo, there has never been an offer," he told Gazzetta dello Sport. "I've never heard anything about Rooney or Cavani either.
"I do not rule out big signings, but only if there is a suitable opportunity.
"We do want a larger squad with adequate cover in all areas in order to avoid the sort of problems we had in January in midfield with all the injuries and suspensions."
Most of PSG's big-money signings last summer came from Italy, with Zlatan Ibrahimovic and Thiago Silva arriving from AC Milan, Ezequiel Lavezzi from Napoli and Thiago Motta from Inter Milan, among others.
However, Leonardo - the former AC Milan and Inter coach - said he could cast a wider net this year.
"The market is opening up," he added. "We may look in Spain or England."