The Wales captain, 32, is heading to the United States next month after the end of a nine-year stay at Real Madrid.
The 32-year-old free agent has been linked to his hometown club following the end of his nine-year stay at Real Madrid.
La Liga president Javier Tebas has a long-running issue with the two clubs.
Real Madrid's new signing Aurelien Tchouameni said Kylian Mbappe asked if he would sign for Paris Saint-Germain, as the 22-year-old was unveiled at Madrid's training ground on Tuesday.