SAIC, which pulled out of a joint venture expected to save the carmaker earlier this year, will now compete with a rival proposal from China's Nanjing Automotive to buy parts of MG Rover.
The carmaker's administrators, PricewaterhouseCoopers, will make the final decision on MG Rover's future after examining the bids.
UK businessman David James is also believed to have submitted a proposal to save the business.
PwC did not name the interested parties but said they planned to acquire all of MG Rover and Powertrain, MG Rover's car and engine-making business.
MG Rover filed for bankruptcy in April under debts of 1.4 billion pounds ($2.5 billion), with the loss of 5,000 jobs after the carmaker was forced to close its production plant at Longbridge in central England.
SAIC said it had signed a letter of intent with Magma Holdings Ltd, a London-based company founded by Leach and former General Motors executive Edward Sabisky.
"Magma intends to acquire all of the assets of MG Rover Group Ltd and Powertrain Ltd," SAIC said in a statement.
Magma also plans to form a new company to restart production at MG Rover's car production plant at Longbridge, it said.
Sources close to the situation told Reuters the Magma proposal involved what they described as "serious" production at Longbridge, although nowhere near the same levels seen before MG Rover collapsed.
The consortium is also proposing to establish a design and engineering center there employing 1,300 to 1,600 people.
Other sources familiar with the situation have told Reuters that production of engines for the convertible MGTF model would probably move offshore under a deal. MG Rover used to supply engines for 14,000 MGTF cars a year.
The Transport & General Workers Union (TGWU) said it backed the SAIC proposal, which it said offered the best chance of saving some jobs at Longbridge.
The Department of Trade and Industry confirmed media reports that officials met with James on Wednesday. The Financial Times said James was seeking an 80 million pound loan guarantee.
A PricewaterhouseCoopers spokeswoman declined to comment.
Leach sued Ford Motor Co. in late 2003 and reached a settlement with the automaker in March. According to media reports, the settlement was $2.1 million. Leach claimed Ford blocked him from accepting a lucrative post as CEO of Fiat Auto after firing him. Ford says Leach quit and had to comply with a noncompete clause in his contract. A U.S. district judge agreed with Leach last year, clearing the way for Leach's appointment to run Maserati. Leach left Maserati in February.