Cavani's contract expires at the end of the season and the striker has informed PSG sporting director Leonardo of his desire to leave the Parc des Princes.
The Uruguay international is the club's all-time leading goalscorer but has struggled with injuries in 2019-20 and fallen out of favour since the arrival of Mauro Icardi.
Tottenham, Chelsea, Manchester United and Atletico Madrid have all been credited with an interest in Cavani, but the Spurs boss refrained from fuelling the reports at a news conference ahead of their game against Norwich City on Wednesday.
However, Mourinho playfully suggested he would be more than happy to bolster his squad with Cavani's PSG team-mate Mbappe.
"I have a very good relationship with Mr Nasser [Al-Khelaifi, PSG president] and Mr Leonardo and I want to keep that great relationship," said Mourinho.
"Good relationships are based on respect and I'm not going to speak about a player from Paris Saint-Germain.
"Unless you want a joke and if they are my friends, they could send Mbappe on loan? More than that, I have nothing else to say."
World Cup winner Mbappe has scored 21 goals in 22 appearances in all competitions for PSG this season.