A number of national newspapers in England suggested on Tuesday that PSG were lining up a summer swoop for England international Rooney.
The club have also been linked with moves for Real Madrid forward Cristiano Ronaldo and Napoli striker Edinson Cavani.
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."
Even if no deal for Ronaldo emerges, one obvious target at Real Madrid would be France striker Karim Benzema, and Leonardo admitted he was keen to bring some French stars into the PSG line-up.
"The idea of seeing the great French players here is something I like," he said. "I'm not necessarily talking about Benzema, but maybe (Samir) Nasri, (Franck) Ribery or (Yohan) Cabaye.
"But I do not know if it is feasible and I have not had contact with any of them."