The two Englishmen faced off in the inaugural World Golf Final in Turkey earlier this week, with victor Rose collecting just under a million pounds and runner-up Westwood netting £622,000. However, these winnings do not contribute to their Race to Dubai totals.
Both men still feel that with strong ends to the season they could squeeze out world number one McIlroy, who is £381,000 ahead of Rose, at the top.
"He's got a bit of a lead on me and is playing a lot of golf now so he's going to be tough to catch, but if I can continue to push the top end of the leaderboard I will give myself a chance and that will be fun," said Rose.
Westwood added: "I have five massive tournaments left and if I can play well for a couple of weeks in China and then in Dubai then I might have a sniff of the Order of Merit.
"I've only won twice this year so I would like to win more before the year is out."
Both men were part of Europe's victorious Ryder Cup team.