Spurs are prepared to sell the long-serving defender this summer as Mauricio Pochettino continues his squad renewal.
Juventus initially led the race to land the England international, who is available at around £20m.
However, PSG have jumped to the front of the queue in recent days and are increasingly confident of completing a deal.
Rose has not taken part in Tottenham’s pre-season tour of Asia as he looks for a new club.
Spurs are hoping to sign Fulham’s Ryan Sessegnon as a replacement for Rose, who has been on the books since 2007.
10 incredible goals wasted in meaningless friendlies
10 overpriced transfers that absolutely worked out
27 essential Fantasy Premier League tips from old winners and experts