President Trump says the feds are getting closer to cracking the kidnapping case of Savannah Guthrie‘s mom Nancy … and the FBI may even have a suspect!

Trump shared the bombshell news with reporters on Air Force One Friday night, saying investigators have made real progress in the investigation. And 47 says he’s not talking about search results … he’s talking about “solutions” in the case.

And get this … When a journalist asked if someone had been identified as a suspect, Trump responded, “Yeah. Could be definitive.”

Trump also said investigators have “very strong” clues, believing “we could have some answers coming up fairly soon.”

Earlier in the day, the Pima County Sheriff’s Office, which is working with the FBI, announced they are inspecting a new message, which KOLD 13 News received. KOLD anchor, Mary Coleman, told CNN the note may have been written by the same person who sent previous letters to the station, TMZ and KGUN 9 News.

TMZ’s alleged ransom letter contained a demand for money in exchange for Nancy’s safe return, but the first deadline passed at 5 PM Friday. A second deadline is set for Monday, February 9.

As you know, Nancy was reported missing Sunday after family members got word she missed a church service and called police, who quickly learned she’d been abducted from her home overnight. Nancy was last seen by her daughter, Annie, on Saturday evening when the two had dinner together.