TechCrunch reported a source with 'direct knowledge of the discussions' as saying that the talks are not at an advanced stage yet as other companies, such as Japanese firm GREE, are also interested in OMGPOP.
The studio has raised around $17m (£10.7m) to date, causing TechCrunch to estimate the firm's acquisition price at between $150m to $250m.
The deal with Zynga is far from a certainty, but if it does go ahead then it would be Zynga's biggest acquisition since the firm listed on the stock market last year.
Zynga's last major purchase came in late 2010 when it bought Words With Friends-maker Newtoy for $53.3 million in cash and stock. Following the deal, Words With Friends doubled its daily active users, helping Zynga increase its mobile footprint.
A deal for OMGPOP would grow this even further, as Draw Something - a social media-focused take on the Pictionary board game - has become a runaway success, attracting more than 30 million downloads on iOS and Android in just six weeks after its release.
The game is said to be adding another 1m downloads every day, and is thought to be making reasonable revenue from paid downloads, in-app purchases and advertising.
Instead of pursuing the acquisition, Zynga could instead look to compete with OMGPOP by launching a drawing game extension of Words With Friends.
But that may take months of development and the title could be well behind the game by the time it launches. Despite being a costly solution, an acquisition of OMGPOP would give the firm a direct route into the market and a growing customer base.
Zynga could look to roll the game into the 'With Friends' line, as Newtoy has already launched Scramble With Friends and Hanging With Friends spinoffs, among other games.
The firm could further take Draw Something beyond mobile platforms and introduce the title to its new social games platform that was launched to reduce the dependency on Facebook.