The plan affecting up to 6 percent of its pharmaceuticals workforce comes on top of a programme to reduce the number of production sites and is part of a larger drive to cut costs, the newspaper said.
Global drugmakers are under increasing pressure from investors to step up restructuring as patents on best-selling drugs expire and governments try to keep a lid on health costs.
NZZ am Sonntag said it received a statement from Novartis saying that the overall number of employees should remain "relatively stable" in 2014.
The paper said that a significant part of the 4,000 jobs will be transferred to India, where Novartis rented an office building able to house 8,000 employees in Hyderabad.
A Novartis spokesman was not immediately available to comment.
Novartis, which will face copycat competition for blood pressure pill Diovan once Ranbaxy Laboratories overcomes regulatory delays for its generic version, posted lower than expected core earnings per share last week.
The company is also conducting a review of its over-the-counter, animal health and vaccines businesses, which lack the global scale of its pharmaceuticals operations.