According to the FA's former executive director David Davies, whose book FA Confidential is being serialised by the Daily Mail, Eriksson made the request following England's quarter-final exit in Euro 2004.
The four players were uncapped by the countries they were born in, and would have legally been able to turn out for the Three Lions due to residency rules.
Edu, who was at Arsenal at the time but moved to the Spanish side Valencia in 2005, has since been capped for Brazil while the Manchester United forward Saha has represented France.
"'I like Carlo Cudicini', Sven told me - an opinion which led to a very serious consideration being given within Soho Square to recruiting Chelsea's Italian goalkeeper," said Davies.
"'Can you also find out about Malbranque, Edu and Saha?' Sven asked me. I wasn't sure what the public reaction would be to an Italian, a Brazilian and two Frenchmen coming into the squad but I did Sven's bidding.
"However, all my discreet enquiries to clubs and agents led to nothing. Miraculously, the moment our interest became known Saha and Edu were called up by their own nations, making them ineligible."
