Speaking to US Weekly, Louis refused to confirm the romance - but voiced his approval of the country pop superstar anyway.
He said: "I'm happy they're good friends."
And bandmate Liam added that he thought she was a "really lovely girl".
The Sun has claimed that Taylor and Harry's relationship is causing division in the band already.
Artist Yoko's relationship with John Lennon has famously been blamed for the break-up of The Beatles.
Watch MTV News on the hour every hour on MTV - Sky Channel 126 and Virgin Channel 134