The Tottenham right-back has been discussing his own and the north London side's aspirations.
And the 25-year-old admits he would love to win the Premier League with the White Hart Lane outfit.
However, the key to success may well be to stay grounded, the defender suggests, especially during such a busy and important time in the season.
Walker told Sky Sports: "I'd love to win the Premier League with Tottenham, I'm not going to say I wouldn't. I've been here six years and when I first joined the club I wanted to achieve things.
"But there's a long way to go, the December period is a very important time to get a good run of form going. Get a good couple of wins together and I think this is make or break time."
It's definitely too soon to talk of the Premier League title for Spurs and the battle for a Champions League place will no doubt prove a fascinating one if the north London side, Liverpool, Arsenal, Manchester City and Manchester United are all in the mix at the business end of the campaign.
Throw in Leicester City, currently flying high, and Chelsea if they are going to bounce back, and you have a very open race indeed.
Walker is right to emphasise the December period - when the games come thick and fast. Over their next five Premier League fixtures, Tottenham face Southampton, Norwich, Watford, Everton and Leicester. All are winnable - but none will be easy.