The music legend is voicing a character and writing a song for the latest installment in the hit animated franchise, and has arranged for Beatrice to sing backing vocals on the track so she features in the movie.
A source said: "Paul is really pleased to be part of the next Shrek film because it's Beatrice's favorite movie."
"He said she can't stop talking about it. He wants to go one step further though and make sure she's part of the film."
"Paul's writing a song for the film and wants Beatrice to sing some of the harmonies. She's quite a musical kid. She's very bright. It will be a dream come true for her."
The 66-year-old musician will lend his voice to a character along with Cameron Diaz and Antonio Banderas in "Shrek 4."
Paul has previously admitted he does impressions of Shrek, who is voiced by comic star Mike Myers in the films, for Beatrice because she is such a fan of the kindly green ogre.
He said: "I'm a huge fan of 'Shrek' as my little girl loves it. I can do a really good impression of him - I put on my best Scottish accent!"
