The 48-year-old supermodel was romantically linked to the One Direction band member shortly after her split from Skepta last year.
But when quizzed about her relationship with the 25-year-old singer, the catwalk icon instantly shut down the conversation.
Speaking on The Jonathan Ross Show, which is set to air this Saturday, the host asked: "There have been a lot of headlines recently connecting you to Mr Liam Payne."
Naomi swiftly replied: "And? I never discuss my personal life. Another name?"
A persistent Jonathan, 58, went on: "Drake? You got quite close to Drake?"
But Naomi was not going to divulge any further details.
She added: "I never discuss my personal life."
The star went on to brush off any attachment to celebrity males insisting she will be connected to a different man she is seen out with every day.
She continued: "I mean, it’s crazy. It’s like one day it’s one person, the next day it’s another."
Jonathan joked: "Who is tomorrow?"
Naomi replied: "That’s what I want to know… For me I laugh. The stories are incredible, it’s humorous… I just get on with my life."
As the host continued to probe Naomi and asked if she was single, she coyly replied: "I don’t want any blind dates, thank you!"
The Sun on Sunday broke the news of Liam and Naomi’s secret romance last month after he had told pals of their “mind-blowing” trysts.
The pair were also pictured eating dinner together while on holiday in Ghana, after they gushed about one another on social media in the comment section of each other's posts.
But is seemed their fling was short-lived as The Sun learned Naomi warned Liam not to get too clingy because she's not after anything serious, and she avoided talking about him at her appearance at WE Day event earlier this week.
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