City's all-time leading goalscorer is due to be out of contract in the summer and has offered little indication that fresh terms will be agreed before then.
Aguero is therefore able to sign a pre-contract agreement with any foreign clubs from this month ahead of a free transfer in July.
According to football agent Bruno Satin, PSG are among the clubs interested in opening talks with the Argentina international.
Speaking to Canal+, Satin claimed that Aguero is a priority target for Pochettino, who succeeded Thomas Tuchel in the Parc Des Princes dugout last week.
Aguero, restricted to just three starts in all competitions this season due to injury, is said to be holding out for a salary of around £240,000 a week. body check tags ::