President Donald Trump's administration is considering a trade package including indefinite tariffs, investment restrictions and possible visa restrictions on Chinese travelers, a source told CNBC Tuesday.

The new package was crafted in response to the findings from a recent investigation of China by U.S. Trade Representative Robert Lighthizer.

The so-called Section 301 investigation was formed to determine whether China's practices were "unreasonable or discriminatory and burden or restrict U.S. commerce."

The proposed package of penalties, which could foment a more adversarial trade relationship with China, comes amid a report from Reuters that the Trump administration is also seeking to impose heavy new tariffs on China.

Trump may impose tariffs on $60 billion of Chinese goods, Reuters reported Tuesday, citing a source who had discussed the issue with the White House.

The potential tariffs would target the technology and telecommunications sectors, according to Reuters, but would not be limited to those sectors.

Politico reported earlier that Trump had rejected proposals for tariffs on $30 billion of Chinese imports, demanding instead even steeper duties on China.

China runs a $375 billion trade surplus with the United States and when President Xi Jinping's top economic advisor visited Washington recently, the administration pressed him to come up with a way of reducing that number.

Trump came to office on a protectionist agenda and his first action as president was to pull the United States out of the 14-nation Pacific trade pact, known as the Trans-Pacific Partnership (TPP).

He has started talks to renegotiate the North American Free Trade Agreement (NAFTA) and most recently imposed tariffs on steel and aluminum imports.

This story is developing. Please check back for updates.

--Reuters contributed to this report.