The two sides are expected to meet during the scouting combine - held from Feb. 27 to March 5 - to discuss a new, short-term contract, Ian Rapoport of NFL Network reports.
Brees is scheduled to become a free agent when the new league year begins on March 14.
Though Brees is now 39 and has played 18 seasons, he remained in MVP contention during the 2017 season while leading the Saints to a division title and one play from the conference championship game.
Brees has said on multiple occasions that he doesn't intend to wear another uniform as long as the feeling is mutual from the Saints. General manager Mickey Loomis said he doesn't anticipate any issues re-signing his quarterback either.