The news comes ahead of a planned visit to India by US Secretary of State Mike Pompeo, Reuters reported.
Last year, Indian authorities told American credit card firms MasterCard, Visa and American Express that they would have to store data locally. The companies were reported to be lobbying the Indian Government in a bid to avoid this requirement.
A few months later, it was reported that India's domestic payments networks RuPay and Unified Payment Interface were gaining ground over MasterCard and Visa.
India is the biggest recipient of H-1B visas, with nearly three-quarters of the annual quota of 85,000 going to its citizens who work predominantly in the tech industry in the US.
The curbs will result in only 10% to 15% of the annual quota being available to Indians.
Indian outsourcing companies like Infosys, Wipro, Tata Consulting Services and Cognizant will be badly affected by the curbs were they to take effect.
The Indian move to store data locally was mentioned as being a barrier to US digital trade by the US Trade Representative in March.
The USTR said in a fact sheet: "In 2018, India published a number of measures that would restrict the cross-border flow of data and create onerous data localisation requirements.
"In October, one such measure was implemented, requiring payment service suppliers to store all information related to electronic payments by Indian citizens within India.
"Much broader restrictions included in India’s draft Personal Data Protection law and draft e-Commerce Policy threaten to undermine the digital economy as a major source of growth for India."
Concerns over data localisation have grown in recent years as multinational companies obtain business contracts abroad. In February last year, Apple agreed to store iCloud data of Chinese customers with a local firm as a condition of doing business in the country.
Recently, when Microsoft acquired code repository GitHub, there were fears expressed that the American spy agency NSA could have access to all the source code residing on the hub. Microsoft has in the past provided the NSA with access to its systems.
If the H-1B quotas are enforced, they would effectively satisfy another stated aim of the Trump administration which, since it assumed office in 2017, has been pushing for changes in the H-1B system in keeping with its policy of "America first".
The changes in the system were announced in January, with one effect being that the proportion granted to foreigners with a master's degree or higher from an US institution would be increased.