The two executives had a phone conversation last week, the sources said. Discussions involving lower-level officials of the two companies are also ongoing.
Page and Cook are expected to talk again in the coming weeks, though no firm date has been set, the sources said on Thursday. One of the sources told Reuters that a meeting had been scheduled for this Friday, but had been delayed for reasons that were unclear.
The two companies are keeping lines of communication open at a high level against the backdrop of Apple's legal victory in a patent infringement case against Samsung, which uses Google's Android software.
Last Friday, a jury awarded Apple $1.05 billion in damages and set the stage for a possible ban on sales of some Samsung products in a case that has been widely viewed as a "proxy war" between Apple and Google.
One possible scenario under consideration could be a truce involving disputes over basic features and functions in Google's Android mobile software, one source said. But it was unclear whether Page and Cook were discussing a broad settlement of the various disputes between the two companies, most of which involve the burgeoning mobile computing area, or are focused on a more limited set of issues.
Competition between Google and Apple has heated up in recent years with the shift from PCs to mobile devices. Google's Android software, which Apple's late founder Steve Jobs denounced as a "stolen product," has become the world's No.1 smartphone operating system. The popularity of the software has been in tandem with patent infringement lawsuits involving various hardware vendors who use it, including Samsung and HTC.
The latest complaint was filed by Motorola Mobility, now a unit of Google, against Apple at the U.S. International Trade Commission claiming some features of Apple's devices infringe on its patents. A previous lawsuit between the two in a Chicago court was thrown out by a federal judge, who said neither side could prove damages.
Apple in recent months has moved to lessen its reliance on Google's products. Apple recently unveiled its own mobile mapping software, replacing the Google product used in the iPhone, and said it would no longer offer Google's YouTube as a pre-loaded app in future versions of its iPhone.
Cook took the helm at Apple a year ago, and Page stepped into the top job at Google a few months before that.
The conversation between Page and Cook last week did not result in any formal agreement, but the two executives agreed to continue talking, according to one source.
Google's Larry Page, who sat out several public speaking engagements earlier this summer because of an unspecified medical condition affecting his voice, has continued to run Google's business.
Apple and Google declined to comment on any discussions.
Copyright Thomson Reuters 2012