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10:30 AM PT -- Sources connected with Jackie tell us her mom jumped the gun. We're told the Bocelli duet was discussed as a possibility, but nothing's written in stone -- especially because Andrea hasn't yet signed on the dotted line for the inauguration -- but everyone has their fingers crossed.

Donald Trump didn't just land Jackie Evancho for the National Anthem at the inauguration -- we've confirmed he's also locked down Andrea Bocelli for at least one song, maybe 2.

Jackie's mother, Lisa, tells TMZ ... the Donald himself called Jackie's manager to invite Jackie to sing the National Anthem on Jan. 20th. We're told it was sorted out Tuesday and Jackie excitedly accepted.

Lisa also says the 16-year-old was asked to do a second performance with Bocelli. It's unclear if he's doing a solo, but it's Andrea Bocelli ... so we're guessing yes.

Jackie's no stranger to big stages. The "America's Got Talent" runner-up performed for Prez Obama twice. She also performed at a charity event Donald attended when she was 11 -- and she even sang with Bocelli last year in Italy.