The Magpies, who haven't won a trophy since 1969, are on an unbeaten run in the Premier League and have climbed to fourth place after eight games into the season.
"If you are asking me what I want to do in the next two years, I would like us to win a trophy," ESPN quotes Pardew as saying.
"That's something that needs to be ticked here. If I can do it, it will be absolutely magnificent with the team.
"If I can't, we want to get as close as we can, to be competitive in the Premier League and keep pushing for a cup, because they are not easy to win."
The North East side take on Wigan Athletic at St James's Park this weekend.