Lady Gaga gives Cher a song for Oscar winner’s new album

Maybe they can share outrageous outfits next. Cher has recorded a song written by Lady Gaga and RedOne for her next album, her first set in 10 years.

The Oscar winner tweeted the good news Wednesday night: “Just walked in from studio! I finished 1st track on new cd &…. ‘Gaga” ‘You Are The Greatest Thing to Me.””

The interpretation of this tweet, according to Idolator, is that Gaga and RedOne gave the song, “The Greatest Thing,” to Cher. For now, it won”t be a duet, although Cher remains hopeful. “Who knows?,” Cher further tweeted. “I did hold her meat purse. Ha ha! One can wish!”

[More after the jump…]

Below is a demo of the song that showed up online last year, which PopDust unearthed. It”s pretty average, but in the right producer”s hands, do you think it could turn into another “Believe?”