Spurs have bounced back impressively from a miserable start to the campaign and look set to finish in the top half of the Premier League table.
They could even qualify for the Europa League but Woodgate believes the targets for next term must be even more ambitious.
The defender has been impressed with the latest arrivals at White Hart Lane and feels Tottenham can put pressure on the leading clubs under the management of Harry Redknapp.
He said: "I want to finish as far as we can up the league. The aim is always to get in the top four and the Champions League.
"We'll see how we do. It's going to be a better team next year, you can see how the team has changed under the manager we have now.
"Robbie (Keane) and Jermain (Defoe) have been good acquisitions for the squad, along with Wilson Palacios, who has been brilliant for us.
"It's taking shape in the training ground and we are starting to do it on a Saturday."
Gomes hails defenceWoodgate's defensive partnership with Ledley King has been a major factor behind a run of six consecutive clean sheets at White Hart Lane.
Heurelho Gomes has also been in fine form of late but the goalkeeper believes it is the back four that deserves much of the credit.
Gomes told Spurs TV Online: "The defence is unbelievable. They play very well all the time, they help us so much for our clean sheets.
"It is the best defence I have played in, they understand the game so much and that is important for us."
Spurs will set a new club record for the fewest number of league goals conceded at home in a single season, which currently stands at 11, if they let in less than two against Manchester City later this month.
"I think we can do it," Gomes added. "Before I came here I wasn't looking for the record, I looked just for the team and winning games. Now we have a chance for the record, it's amazing."