'drew increased attention' is correct and can be used in written English.
You can use it when speaking about something that received more attention than usual. Example: The singer's solo debut drew increased attention from the world of music fans.
The issue of betting in tennis drew increased attention from the sport's governing bodies after an online bookmaker voided all wagers on a 2007 match involving Nikolay Davydenko.
This drew increased attention to tribal areas in northwestern Pakistan that were being used as a base and sanctuary for Taliban operations in Afghanistan.
She drew increased attention to Spanx when she appeared as a contestant on the 2004 05 reality television program Rebel Billionaire, which was hosted by the British entrepreneur and philanthropist Sir Richard Branson.
Charges against Mr. Moffat drew increased attention because he was a high-level executive at the International Business Machines Corporation, where he once was considered a candidate for chief executive during a three-decade career.
With the former (social networking), the reason had to do with the $1 billion acquisition of Instagram, which drew increased attention to the category.
Commentators noted Beck's actions triggered the Streisand effect; his suit against the website drew increased attention to it.
But the trade drew increasing attention as the index continued to spike, multiplying JPMorgan's potential losses if it had to pay out on the insurance.
The tiny completion rates for most MOOCs drew increasing attention.
Pre-production continued on Iris as it drew increasing attention not only in Korea but also in Japan due to Lee's involvement.
And that is drawing increased attention from economic development officials.
Martin, who leads the N.F.L. in rushing with 613 yards, has drawn increased attention from opposing defenses, making them more susceptible to fakes.
