The 32-year-old striker will leave St James' Park when his contract expires at the end of next month.
The Nigeria international has scored 79 goals in 397 appearances during his 14-year spell with the Magpies.
"Shola will go down as having been a very important person for this football club," Pardew told the Sunderland Echo.
"I hope, one day, that they bring him back. His professionalism, and the way he articulates himself, is something he should be very proud of."
Ameobi has been linked with a move to fellow Premier League side Hull City.