However, the 'If I Could Turn Back Time' singer is not sour about it at all. In fact, the music legend has said nothing but positive words about her fellow wig-wearing songstress, and has recently been using social networking site Twitter to tell Gaga that she is greatly enjoying the "amazing" 'Cheek To Cheek' - Gaga's new collaborative studio album with veteran singer Tony Bennett.
Cher wrote to Gaga a few days back: "So f*cking proud of you Gaga. I heard (and saw) amazing CD collaboration 'Cheek To Cheek' with the forever hip Tony Bennett. Babe, you're channelling jazz greats and killin' me."
One fan then asked Cher if she had ever sang with fellow veteran musician Bennett; she answered, "Tried. I love him. I was desolate. The song didn't work for both of our ranges. It's OK. Gaga and Tony Bennett knocked it out of the park."
The ever-honest 'Moonstruck' actress then wrote to her two-million-followers: "No-one could make me say anything that I don't believe, when it comes to art. Gaga sang her ass off! Pure heaven talent. F*ck haters".
Later on, Gaga replied, "You know Cher, that level of support coming from you means more than you will ever know. Your confidence is the mark of a true legend. Love you."
The 'Bad Romance' singer - whom has covered Cher's 1966 US#2 million-seller 'Bang Bang (My Baby Shot Me Down)' as a bonus track for 'Cheek To Cheek' - added, "It's a supreme honor to sing 'Bang Bang', that song time-travelled and continues to inspire, I wish to honor your legacy with every breath."
Clearly appreciative of the support from Cher, Gaga - whom affectionately calls her fans "Little Monsters" - then asked her whopping 42-million followers to get a Cher hashtag to trend on Twitter: "Trend it Monsters. Let's show Cher how much we appreciate her #MonstersLoveCher Now that's what I call class!"
- Cher tweeted about a sad childhood memory: "When I was four, my 6-foot-1 father beat me with a belt. I looked up at him, shook, and wondered what did I do. How can you do this? I'm so tired and I love you. Why?"