The bid for the English Premier League side marks a potential challenge to an earlier planned acquisition by Lander Sports Development, which said in January that it was taking a stake in the club.
Southampton take on Manchester United in the final of the League Cup on Sunday, after having beaten Liverpool at Anfield last month in the semi-finals. The Saints last played a major final at Wembley Stadium in 1979.
The new bid comes as China's government has ramped up scrutiny of outbound deals and capital outflows, with some dealmakers saying Chinese firms are unable to finalise investment plans because they cannot get Beijing's sign-off.
Lander declined to comment. Amer International did not immediately respond to requests for comment. A CITIC Securities spokewoman said in a written comment the firm was not yet involved in any investment of this kind.
The new consortium, which also includes other private investors, was looking to buy 100 percent of the English south coast club for close to 2.1 billion yuan, the person added.
Industry insiders say a number of sports-related deals have hit hurdles after Beijing said it would rein in risks from "irrational" outbound investments, with particular focus on sectors including hotels, entertainment and sports.
"It's against the will of the President to acquire an EPL club right now," said the person with knowledge of the deal.
Should the deal go through, Southampton would join fellow English clubs Manchester City, West Bromwich Albion and second-tier sides Aston Villa, Birmingham City and Wolverhampton Wanderers in having Chinese investment.
Southampton, who are currently 11th in the Premier League, have been a model of success since being saved by the late Swiss billionaire Markus Liebherr in 2009. Liebherr's daughter Katharina is the Premier League club's current owner.
A Chinese deal for Italian club AC Milan, which was held up as the buyers struggled to get approval from Beijing, was now expected to be finalised in early March, sources told Reuters this week.
(Reporting by Peter Rutherford in SEOUL and Adam Jourdan in SHANGHAI; Additional reporting by Jackie Cai and David Lin in SHANGHAI; Editing by Greg Stutchbury)
