The Brazilian scored in Spurs' 2-1 victory over Sunderland on Saturday, easing the pressure that was building on manager Andre Villas-Boas.
Paulinho told reporters: "It's a big game at home and we must think that if we play the same as we did against [Manchester] United, we have a big chance to win at home against Liverpool.
"It's still very compact at the moment. Arsenal have gone a distance. Obviously Arsenal have three important fixtures in the next games with Chelsea, Manchester City and Everton, but we just want to be near them and get ourselves into the Champions League positions.
"At the moment, we are fighting our way back, but we want to be there at the end of the season."
Spurs find themselves sixth in the Premier League table, three points behind second-place Liverpool.