The contract is reportedly a one-year deal worth between $5 million and $6 million.
Jagr's agent, Petr Svoboda, told the Newark Star-Ledger that the deal will become official soon.
"The deal is very, very close, but it's not finalized yet," Svoboda told the Star-Ledger. "[Devils GM Lou Lamoriello] will let you know as soon as it's complete."
The 42-year-old Jagr, who led the Devils in scoring with a 24-goal, 67-point season, said after the team's season ended that he'd like to return in 2014-15.
Svoboda could not immediately be reached by phone or email for comment.