The Liverpool Echo says the Blues have been alerted by the Benin international's declaration that he wants to leave the French outfit this summer.
Manager David Moyes went on a scouting mission to watch the 26-year-old last season and must now decide whether to follow up his interest with a bid.
Reports in France suggest PSG will demand a fee of around £8million.
"I want to move out of PSG," Sessegnon said. "They know it, I know it."
Tottenham and Sunderland are also believed to be interested in a player who can play on the wing or just behind the striker.