The Yankees were awarded a waiver claim on Lilly -- which, considering New York has the best record in a league Lilly doesn't play in, means no other club made a claim -- but the Dodgers told them they had no intentions of trading him, according to reports.
The Dodgers believe they still have a chance to make the playoffs while sitting 6 1/2 games back of the National League Wild Card lead and would also like to sign Lilly long-term, ESPN.com and FoxSports.com wrote.
"Both the Dodgers and Ted would like Ted to stay," Larry O'Brien, Lilly's agent, told ESPN.com.
The 34-year-old Lilly is making $12 million in the final year of his contract this season, which comes out to about a prorated share of $2 million if he's acquired for the stretch run. The New York Daily News reported that even though the Yankees couldn't get Lilly the first time around, they'll "continue to push to make a deal."
The deadline for players to be eligible to play in the postseason passed on Tuesday.
Lilly, a member of the Yankees from 2000-02, is a combined 8-9 with a 3.59 ERA in 24 starts with the Cubs and Dodgers this season.