The 'Strip That Down' hitmaker has admitted that if he and the former Girls Aloud singer, 33, appeared on a track together, they could risk sounding ''cheesy'' like former couple, ex-glamour model Katie Price, 39, and 'Mysterious Girl' singer Peter Andre, 44, who famously released their own version of 'A Whole New World' from Disney's 'Aladdin' in 2006.
The One Direction star said that the brunette beauty - who gave birth to the couple's son Bear in March - probably wouldn't allow him to collaborate with her anyway.
According to The Sun newspaper, the 23-year-old heartthrob said of the chances of them recording a song together: ''I think sometimes those things can go a bit cheesy. We're not going to do the Katie Price and Peter Andre.
''She wouldn't have me anyway. She'd kick me off. I'm lucky to be here still.''
Meanwhile, the pair are already thinking about giving their three-month-old son a brother or sister.
Asked if they plan to add to their brood, Liam said: ''We have spoken about this. We will see what happens ... We are in a routine now and loving life. We sit round with Bear, watch old films like Ritchie Rich and Stand By Me, have a laugh.''
And the hunk went on to praise his partner for being so ''amazing'' and strong throughout the whole pregnancy and the birth.
He added: ''She's very headstrong. She's a strong woman. We had Kimberley Walsh round and she couldn't believe that we'd got baby Bear into such a good routine.
''Cheryl's just been amazing. She doesn't want to miss the close contact with him. And the thing people don't know is she has done it all herself . When she first got pregnant, I couldn't keep up with everything.''
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