Chargers general manager A.J. Smith confirmed he got a call from Giants GM Ernie Accorsi on Tuesday.
"They would like to move from four to one," Smith said on Wednesday.
Smith wouldn't discuss specifics.
"Anything we discuss is football business between the two of us," Smith said.
The Chargers worked out Manning and the other two highly regarded quarterbacks in the draft, Ben Roethlisberger and Philip Rivers.
But trading down and acquiring additional picks would allow San Diego to address its many other needs. The Chargers don't have a left tackle or a standout wide receiver or defensive end.
The Chargers also had the No. 1 pick four years ago and traded it to Atlanta the day before the draft. Atlanta got Michael Vick, while San Diego took LaDainian Tomlinson at No. 5. The Chargers also got receiver-returner Tim Dwight and two other picks.
Also Wednesday, the University of Pittsburgh's Larry Fitzgerald, one of the top receivers in the draft, visited the Chargers.
"This was kind of like a recruiting visit today," said Fitzgerald, who met with coach Marty Schottenheimer and receivers coach James Lofton. "It's fun. I got to out and have lunch with
Coach Lofton, somebody I looked up to as a child."