Florentino and coach Zinedine Zidane have agreed they need to buy a "new No9" when the winter market opens with the Real squad short of attacking options.
The president has settled on Cavani, knowing he will be available in the New Year after his fallout with PSG teammate Neymar.
Don Balon says Zidane, however, isn't so sure, insisting Karim Benzema - when fit - would be his first-choice No9. The Frenchman would prefer a 'reserve signing' capable of covering for injuries and suspension when needed.
Florentino has told his coach the attack must prove itself over the coming months, or he will firm up his pursuit of Cavani. He has already confirmed his interest to PSG president Nasser Al-Khelaifi, after speaking with him about the availability of goalkeeper Keylor Navas.