The 39-year-old Englishman has recorded 13 top-10 finishes in golf's blue riband events, most recently a tie for third at the Masters in April, and he is among the favourites for this week's U.S. Open at the Olympic Club.
"Majors are the only thing missing that I haven't won," world number three Westwood told reporters while preparing for Thursday's opening round. "That's why I concentrate on winning.
"Maybe I'll never win one. Maybe I will. I could. I've got no answer to that. Keep working hard and trying to get myself into the position. If it happens, it happens. If it doesn't, it doesn't."
Westwood has long been regarded by his peers as one of the best ball-strikers in the game and he is ideally suited to the traditional set-up for U.S. Opens with narrowed fairways, thick rough and firm greens.
"It really does test you tee to green," Westwood said of the hilly, par-70 Lake Course at Olympic. "It's a good driver's golf course. If you can drive it in play a lot then it gives you a chance to score.
"Not that you hit that many drivers around here, but I think any U.S. Open test is more of a tee-to-green examination than week-in week-out tournaments."
When told that many people felt that Olympic's challenging Lake Course was a perfect match for Westwood's game, the Englishman smiled.
"I'm delighted that they think that," said Westwood, who tied for seventh when the U.S. Open was last held at Olympic in 1998.
"I can't figure out what's my kind of golf course and what isn't anymore. My game seems to be fairly well suited to most golf courses."
The straight-hitting Englishman has recorded four top-10s at the U.S. Open, including two top-three finishes in the last four years, and he arrived at Olympic boosted by his 22nd European Tour at the Scandinavian Masters last week.
"It is nice to come off a win, with that confidence," he said. "I expect this week to be a tough test. I've seen the golf course over the last couple of days and it's difficult, like all U.S. Open tests normally are.
"This is one of the tougher ones. It sets up really well and tests every aspect of your game."
Westwood will tee off in Thursday's opening round in a high-profile grouping with world number one Luke Donald and defending champion Rory McIlroy.
"It's a good group to be in. We'll all enjoy it, I would imagine," said Westwood. "It's nice to play with people you know and people you've got something in common with and you get on with."