The Argentine, who is said to be holding out for a salary of around £240,000-a-week, is due to be out of contract in the summer, therefore the 32-year-old veteran is able to sign a pre-contract agreement with any foreign clubs ahead of a free transfer in July.
According to football agent Bruno Satin, PSG are interested in opening talks with the Argentina international.
Speaking to Canal+ via The Sun, Satin said that Aguero is a prime target for Pochettino, who succeeded Thomas Tuchel last week.
The Parisians have already a number of world-class talents in their ranks, with the likes of Kylian Mbappe and Neymar, while Barcelona ace Lionel Messi has recently been linked.
Aguero has made just three starts in all competitions this season due to injury.