"I think this England thing is becoming a bit of a problem for the manager. It might be a good time to let Gareth have it. I know him very well and he has the attributes to do it," Pardew told the BBC.
"I've never been offered the job. If I'm offered the job... I'm English, would I turn it down? I don't know. I think I've got the experience to do it.
"I think I can do it one day. I don't know if this is the time. I've just got to hope that at some point we get it right."
During his 18-year managerial career, Pardew has come up against some of the most successful managers in club football and said he was proud to be able to pit his wits against them.
"You earn the right to get in that position and I respect that," the 55-year-old said. "The Klopps, the Guardiolas, the Mourinhos -- they've earned the right to be at those football clubs. Maybe I haven't.
"It's been a long road for me to get to this level and I'm very proud to be here. I do enjoy going up against them (the elite managers) -- I've beat a few of them."
Ninth-placed Palace travel to face champions Leicester City in the Premier League on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
