Officials from the Potteries club are in negotiations with the Ligue 1 team about the 24-year-old and are optimistic they can reach an agreement which would bring the former Real Madrid player to the Bet365 Stadium.
Jesé, wholast summer, has made just one league start for the French side to date and spent the second half of last season on loan at Las Palmas.
The then Middlesbrough head coach Aitor Karanka had hoped to bring him to England in January, but the Teessiders were unable to complete a deal.
Meanwhile,are close to completing the £5m signing of Joselu from Stoke. The Spanish striker, who spent last season on loan at Deportivo de La Coruña, is reported to be on Tyneside for a medical on Monday.