Woods has not won a major since the 2008 US Open, but has a good record at this year's venues, having claimed four US Masters titles at Augusta, the Open at Hoylake in 2006 and the 2000 US PGA Championship at Valhalla.
"He also came a close runner-up the last time the US Open was staged at Pinehurst," Montgomerie told BBC Radio Five Live. "I thought last year was important for Tiger Woods to win a major and he's running out of time, there's no doubt, to beat Jack Nicklaus' record in majors (Woods has 14, Nicklaus won 18).
"The trouble with Tiger is that he just has not been aggressive enough over the weekends. He has played safe golf - he hasn't attacked. The safe game now has gone. This is a very aggressive game we play now.
"When he first came on the scene he was 30, 40 yards past everyone, now he's sometimes 30 yards behind. That's a big difference and therefore he cannot win majors playing safe any more."
Woods has recorded nine top-10s since his last major victory in a play-off with Rocco Mediate at Torrey Pines, and three-time major winner Padraig Harrington believes he will eventually surpass Nicklaus.
"I do agree the less he wins then the harder it gets. He is starting again - it's like he's never won one," said Harrington, whose 2008 US PGA victory remains his last European Tour title.
"I just believe, though, that because he has competed so much, if he gets one then the others will come reasonably soon after and he will get there."
:: The full interview with Montgomerie and Harrington will be broadcast in Five Live Sport from 7pm on Thursday.