But The Beatles Story at Liverpool's Albert Dock is to approach him to ask if he will loan it to them to put on display alongside the Harrison guitar, which they own.
And they estimate their guitar could now reach £500,000 if it went up for auction.
Jerry Goldman, director of the Beatles Story, said: "We are thrilled to see such a high value placed on Beatles memorabilia.
"This acoustic guitar is a very special instrument as it's the guitar on which Paul learned his first chords.