The Magpies are eager to reward Gordon for an outstanding season last time around.
The winger made his way into the England squad for Euro 2024, even though he was a peripheral figure at the tournament.
According to The Athletic, Newcastle want to tie down Gordon for a long time to come.
The winger had been linked with a move to Liverpool earlier this summer, but no deal materialized.
He currently has a contract that expires in 2026, which Newcastle would prefer to extend.