The 40-year-old Fijian, who extended his run of consecutive top-10 finishes in PGA Tour events to 12 with his three-shot victory in the Pebble Beach National Pro-Am on Sunday, believes he would be fortunate to overhaul Woods by the end of this year.
"I want to be number one before I finish playing competitively," Singh told reporters after clinching his third PGA Tour title in his last nine starts. "But it's a hard feat to take Tiger off the top, because he is playing well too.
"If I keep playing like I'm doing now, I have a shot -- maybe not this year, but in a year or two."
"My goal is to go out there and just try to beat the field every week. But I'm not going to be pushed to answer questions about me and Tiger."
Twice major winner Singh, renowned for the hours he puts in on the practice range, has never made any secret of his aspirations to dislodge Woods as the game's leading player.
"Right now, I feel I've got to win more tournaments to get to number one. Finishing top 10 is not going to get me there," he said after tying for third at last week's Phoenix Open.
Last year, Singh ended Woods's four-season reign as the PGA Tour's leading money winner and the Fijian's win on Sunday lifted him to the top of the 2004 standings with $1,966,000 from four tournaments.
He also leads the 2004 PGA Tour stroke averages with 68.15 after 16 rounds, but steadfastly refuses to accept this makes him the game's best player.
"My ranking doesn't say that," he said. "I'm number two and I'm playing the best I can."
"And even though I'm playing pretty good, I'm more concerned with how I'm playing week-in and week-out."
Singh, who clinched his 16th PGA Tour career title on Sunday and his 38th worldwide, is just two away from the tour record of 14 consecutive top-10 finishes set by Jack Nicklaus in 1977.
His peers readily acknowledge he is the player to beat whenever he tees off in a tournament, in much the same way that Woods created a dominant aura between 1999 and 2002.
"It kind of reminds me of the streak Tiger was on a few years ago when he won four majors in a row," said Jeff Maggert, who finished second behind Singh on Sunday with a final-round 69.
"It was like all he had to do was show up, and he was going to shoot five or six under. That kind of reminds me of the way Vijay is playing."
Such talk will hardly bother Singh, who has to be rated a clear favourite for all four of this year's majors based on current form.
The winner of the 1998 U.S. PGA Championship at Sahalee and the 2000 U.S. Masters will continue to do things his own way, keeping his focus well away from media speculation and spending as much time as ever working hard at his game.
Nine-times major champion Ben Hogan was one of Singh's idols, as much for his ruthless work ethic as for anything else.
"I've read every book he wrote," Singh said of Hogan, who won the first three majors of 1953.
"He never stopped practising. There's a guy that worked. He found it in the dirt. That's the way I want to be."