The search engine giant is planning to replace the company head with its advertising executive Dennis Woodside, according to Bloomberg.
Woodside, a former AOL employee, will allegedly oversee the integration of the two businesses, and continue reporting to Google CEO Larry Page and CFO Patrick Pichette.
Google's $12.5bn (£7.7bn) buyout of Motorola was given the go-ahead by regulators in Europe and North America last week. The telecoms company will continue to run as a separate business, with other Android partners unlikely to be affected by the merger.
Motorola's extensive catalog of mobile patents will help Google ward off intellectual property lawsuits from Apple, which has maintained a bitter copyright battle against the Android operating system.
Motorola and Google have refused to comment on reports that Jha is to be replaced as CEO.