The two companies are keeping the lines of communication open at a high level against the backdrop of Apple's decisive legal victory in a patent infringement case against Samsung, which uses Google's Android software.
A jury awarded Apple $1.05 billion in damages last Friday 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's unclear whether Page and Cook are 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.