Speaking to the Daily Star, the reality TV star said she would like to follow the lead of Caroline Flack, who is reportedly in a relationship with Payne's bandmate Harry Styles.
Pope declared: "There is a really good looking one in One Direction - Liam! I would love to go out on a date with him.
"Maybe me and Caroline could have a little double date together. Her with Harry, me with Liam. There could be a One Direction cameo in TOWIE."
Praising the Xtra Factor presenter, Pope added: "Me and my friend keep joking and calling each other Caroline because we go out with younger men.
"But I say 'go Caroline', because Harry is fit. If I was a bloke I'd fancy her because she's just herself and comfortable with that - and I love her hair."
Her most recent relationship with fellow TOWIE star Kirk Norcross - who is seven years her junior - ended in July.
But Pope admitted that she could never embark on a long-term romance with a man younger than her, adding: "He was too young for me. He was 23 and I was 29. I think you start to notice the age difference when you get to that point where you want to get married and have kids."
> Lauren Pope: 'I can never be friends with Kirk Norcross'
Watch the video for 'What Makes You Beautiful' by One Direction below: