(Reuters) - A China-backed private equity fund will decide this week whether to seek U.S. President Donald Trump's approval for its proposed $1.3 billion acquisition of U.S. chipmaker Lattice Semiconductor Corp (>> Lattice Semiconductor Corp), people familiar with the matter said on Tuesday.

Buyout firm Canyon Bridge Capital Partners has spent close to eight months trying unsuccessfully to persuade the Committee on Foreign Investment in the United States (CFIUS), which scrutinizes deals for potential national security threats, to clear the deal.

Critics of the deal worry that technology gained through the acquisition could be used by China's military, but the companies have argued that it poses no such risk.

The U.S. president has the final authority to suspend or prohibit such investments.

This would be the first such case to hit Trump's desk if the merger partners decide to seek his review, and the fourth time in the last three decades that a CFIUS case would go to the White House. U.S. presidents have sided with the committee to block the past three questionable deals.

The Lattice deal's woes underscore a U.S. drive to prevent the transfer of sensitive technology to China. Chinese suitors have faced intense regulatory scrutiny in their pursuit of U.S. chip makers, which has jettisoned some deals in recent years.

The latest 75-day CFIUS review of the Lattice deal, the third since it was announced in November, expires at the end of this week.

The two sides have decided to not seek an extension from the committee, and instead may take the deal to Trump for review, as the regulations allow, the sources said.

The sources asked not to be identified because the deliberations are confidential.

No final decision has been made, and Canyon Bridge and Lattice may opt to terminate the deal, the sources said.

Lattice Chief Executive Darin Billerbeck, who would keep his job if the merger is completed, is in favor of taking the deal to Trump for review, one of the sources said.

Lattice and Canyon Bridge declined to comment. A CFIUS spokesman did not immediately respond to a request for comment.

U.S. regulatory scrutiny of the Lattice deal grew after Reuters reported in late November that Canyon Bridge, based in Palo Alto, California, was funded partly by cash originating from China's central government and had indirect links to its space program.

Portland, Oregon-based Lattice makes programmable chips known as "field programmable gate arrays" that allow companies to put their own software on silicon chips for different uses. It does not sell chips to the U.S. military, but its two biggest rivals, Xilinx Inc (>> Xilinx) and Intel Corp's (>> Intel Corporation) Altera, make chips that are used in military technology.

The companies have extended their agreement to the end of September.

Trump's approach to relations with China has been mixed. He has criticized Chinese trade practices but also wants Chinese cooperation in tackling North Korea's nuclear ambitions.

In the most recent example of a direct rejection by a U.S. president of a CFIUS application, Barack Obama in December blocked China's Grand Chip Investment GmbH from acquiring German semiconductor equipment supplier Aixtron SE (>> AIXTRON SE).

(This story removes extraneous 'to' in fifth paragraph.)

(Reporting by Greg Roumeliotis in New York and Liana B. Baker in San Francisco; Editing by Richard Chang)

By Greg Roumeliotis and Liana B. Baker