New York originally had four men on its initial list of replacements. Two of the other three (Wade Phillips, John Pease) have been eliminated and the other (Vince Tobin) apparently isn't being seriously considered by the Giants. Phillips accepted the defensive coordinator post in Atlanta, reportedly hopeful that he'll become the Falcons head coach when Dan Reeves leaves, rumored to be as early as after this coming season.
Pease was promoted to defensive coordinator with the Jaguars and is staying put. Tobin interviewed with New York four days after Fox was hired by Carolina, but didn't really impress anyone. That leaves Lynn, and while the Giants initially favored someone with coordinator experience (like LBs Coach Tom Olivadotti, who was also given some consideration), it appears that the highly-energetic Lynn is in the driver's seat. He could be named Fox's replacement by the end of the week.
Lynn, a standout defensive back with the Jets for eight seasons, has never been a coordinator, but has been a defensive assistant for 15 seasons. He served in Arizona as LBs and DBs coach from 1987-93, was with Tampa as DBs coach in 1994-95 and had the same duties in San Francisco in 1996. He's been the Giants' secondary coach since Jim Fassel took over in 1997.