The Daily Star says from today they can open talks with the England star, who is out of contract at Arsenal in the summer.
Walcott â€“ a hat-trick hero in the 7-3 defeat of Newcastle on Saturday â€“ wants to stay with the Gunners.
But the North London club are refusing to meet his Â£100,000- a-week wage demands.
PSG are backed with Â£37bn worth of Arab oil money and would be able to offer the 23-year-old double what he wants at the Emirates.
Only overseas clubs can offer this to Walcott and the French giants are at the head of the queue.