A win for Swansea would put them within a point of Tottenham having played a game more when the two sides meet this week.
Cork told the South Wales Evening Post: "If we can get a result there and go just one point behind them, that would be brilliant.
"That's our next target — to get a result against Tottenham on Wednesday."
It took a late goal for Spurs to defeat Swansea City just before Christmas courtesy of Christian Eriksen, but Swansea seem to have a habit of giving the sides pushing towards the top of the table a hard fought game.
They have managed to do the double over Manchester United this season, and have beaten Arsenal at the Liberty Stadium. They also managed a smash and grab win over Southampton at St Mary's when it looked as if their form had taken a bit of a dip.
The game reunites Cork with old boss Mauricio Pochettino but for opposite sides, as Cork worked under the Tottenham Head Coach at Southampton.
The weekend's win over Burnley means they have leapfrogged West Ham United into eighth place, and a win over Tottenham could put them in contention for a place in Europe next season - with Spurs still hoping to do enough to qualify for next season's Champions League.
A win for Swansea could give them a great deal of momentum in the league, with a home clash against Liverpool the next league game up for them after their trip to White Hart Lane. If they manage to get a win from either of those two games, they will have come through a pretty difficult run of fixtures with a decent points tally to show for it.