European competition officials have been investigating the US tech giant for years over alleged monopolistic practices involving its search engines, but any resolution has been elusive. Three successive proposals by Google for an amicable settlement have been rejected.
Pichai will meet Vestager next week in Brussels, the source said yesterday.
Vestager last year sent a "statement of objections," saying Google had diverted traffic from rival price-comparison services like Kelkoo, which operates in several European countries, to favor its own comparison shopping service.
If no agreement is reached, and the group is found to have broken the EU's antitrust rules, it could face fines amounting to billions of dollars.
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Pichai became Google's chief executive officer during a restructuring last year that installed a new holding company, Alphabet, as Google's parent.