The report was sent to Mr Clinton in the last few days, and is destined for Congress.
The report says India and Pakistan might also follow China's example, and that Russia could resume placing multiple warheads on missiles - a practice currently outlawed by the Start-2 disarmament pact.
It also predicts that the US could be within range of ballistic missiles developed by North Korea, Iran and Iraq by 2015 - or even sooner in the case of North Korea.
President Clinton has said he will decide soon on whether to go ahead with the National Missile Defence (NMD) system.
Arms race
The leaked report, from the Central Intelligence Agency (CIA), makes no recommendation for or against NMD - although it echoes critics in the US and abroad who have warned of a new arms race.
The report was sent to Mr Clinton in the last few days, and is destined for Congress.
The CIA says China will expand its nuclear arsenal whatever the US decides on NMD, but will go further if the decision is in favour.
China currently has around 20 intercontinental ballistic missiles, but this figure could increase to 200 if the US shield is built, the CIA says.
Commenting on the leaks from the report on Thursday, the US State Department said NMD would not undermine the existing Russian or Chinese nuclear deterrents.
"The system that we're talking about is designed to deal with emerging long-range ballistic missile threats from states of concern," said spokesman Richard Boucher.
The states of concern, formerly referred to as "rogue states" are North Korea, Iran and Iraq.
Chinese assistance
The Pentagon has hinted this week that technical problems could mean that NMD will not be able to meet its 2005 deployment goal.
The plan has been criticised by European countries, as well as Russia and China.
A separate, unclassified CIA report released this week accused China of stepping up support for Pakistan's missile programme, and assisting missile development programmes in North Korea, Iran and Libya.
"The Chinese have taken a very narrow interpretation of their non-proliferation commitment," the report said.