During an appearance on Mad Dog Sports Radio, general manager Mickey Loomis confirmed the Saints have "had some conversations" with the All-Pro receiver regarding a new deal.
Loomis failed to disclose details of the discussions or whether they were ongoing, but claimed he wanted to make Thomas "a Saint for a long time."
The 26-year-old wideout, who is entering the final year of his rookie contract, said in May he believes the two sides will handle discussions professionally.
Thomas is already one of the NFL's premier receivers, surpassing 1,000 receiving yards in each of his three seasons. He led the league with 125 receptions in 2018 and added 1,405 yards and nine touchdowns.