The 31-year-old's current deal expires in 2014, but Pardew has revealed that he would be keen for that to be extended.
Pardew told the Evening Chronicle: "He's still got another year here with us.
"And I don't see a problem extending that. We'll see."
"I think the bottom line with Shola will be how long he wants to stay at one club, because he's been here all his career.
"I hope he wants to stay, but that'll be his decision."
Ameobi, whose younger brother Sammy is also part of the first-team squad, has spent his entire career at St James' Park having come through the youth ranks.
He made his debut for the Magpies in 2000 and has since played over 350 games for the club.