Spurs are ten games unbeaten in the Premier League and lie third in the table, seven points off the early pace set by Manchester City. They are being discussed as potential title challengers - a remarkable turnaround, considering they lost their first two league matches, shipping eight goals in the process.
Gallas, who has made just one appearance in the Europa League this season because of injury, insists Tottenham have every right to aim high - but has told his team-mates they must be wary of a charge from resurgent rivals Arsenal.
"We have the look of the champion," he said in The Times. "I have won trophies and I know what it feels like to win and it is quite possible to do something here too. Against West Brom and Fulham we have not played as well. It was the same when I was at Chelsea when sometimes we did not deserve to win a game, but with luck we won 1-0 or maybe 2-1, and it is a little bit like that with Tottenham.
"You play for success, you play to lift yourselves, so now we have to believe in ourselves, work hard to try and catch City. It is very wonderful to see how we play and we can win every game. But we should not forget that City are on top and Arsenal are back. It is very important to show again what we can do this season."
Meanwhile, Tottenham boss Harry Redknapp has hailed Ledley King's impact this season, which suggests he may be offered a new contract. King's current deal is due to expire at the end of the campaign, and reports indicate he will earn an extension if he plays in more than 20 games.
"Friday morning will be the first time I see Ledley. He won't train at all," Redknapp said in the Daily Star. "The medical staff will nurse his knee to get him back in shape ready to play for the next week. It's amazing how he can do that.
"It just shows you how good he is. He would have been one of the best centre-halves in the world if he hadn't had these injuries for so many years. He's an amazing player. He can't do too much. I don't know if he can even swim. He just takes it easy all week and we then hopefully wheel him out again the next Saturday."