The source said the issue was the main topic of discussion at a meeting between Russian Finance Minister Alexei Kudrin and U.S. Deputy Secretary of the Treasury Robert Kimmitt June 20.
The proposed restrictions would be introduced for national security reasons and would concern investment in strategic sectors of the U.S. economy.
"First of all, the restrictions could affect Russian and Chinese companies," the source said, adding that amendments to the foreign investment bill are currently under consideration in the U.S. Senate.
The source said the amendments, envisioning an increased period and a more complicated procedure to consider applications, as well as other toughened measures, could come into force this fall.
The source said the law would also allow backtracking on previously issued permissions if a company is shown to have been involved with terrorism or has submitted false information.
If approved, the law would appear to contradict a statement made by Kimmitt in June, when he said that U.S. authorities would urge Russia to invest more money from its reserve and national welfare funds into the American economy.
"Russia has recently approved the transformation by 2008 of its oil stabilization fund into a reserve fund and a fund for future generations, sometimes called a national welfare fund. The current oil stabilization fund operates on the basis of publicly available investment guidelines, and we hope that that will also be the case for the fund for future generations, especially if it too is invested abroad," Kimmitt said.
As of June 1, Russia's stabilization fund stood at 3.141 trillion rubles ($121.7 billion), up 3.8% in June.
"As they look to make decisions about investment opportunities abroad, we want to make sure that they understand that we are open to investment," he said.
Kimmitt said then that in May, U.S. President George Bush released an important policy statement making clear that America is open to foreign direct investment, adding that this was the first U.S. government open investment statement in 16 years.
"And the Commerce Department released statistics last week that indicate foreign capital inflows to acquire or establish a business in the United States jumped 77 percent to over $160 billion in 2006. That's the highest level since 2000," he said.
Kimmitt said that China and Russia, together with the Gulf Arab countries, are three of the largest repositories of sovereign wealth funds, and each has taken steps to diversify their sovereign holdings.
"We want to be sure they consider investment opportunities in the United States as part of that asset diversification strategy, together with efforts to open their economies to greater participation by U.S. and other foreign firms," he said.
Current Russian investments in the U.S. total more than $15 billion.