Matty Healy Is 'Tuning Out the Noise' After Taylor Swift's 'Tortured Poets Department' Release: Source (Exclusive)

The past stays in the rearview mirror for Matty Healy.

The 1975 frontman is "tuning out the noise" amid renewed interest in his former relationship with Taylor Swift following her latest release, The Tortured Poets Department, a source tells PEOPLE.

Though fans have speculated Healy, 35, is the subject of a number of songs on the pop superstar's new album, Swift, 34, does not explicitly mention him by name.

The British musician remains focused on his band — which wrapped their Still ... at Their Very Best tour in March — as they begin writing for the follow-up to 2022's critically acclaimed Being Funny in a Foreign Language.

Healy has made one comment on Swift's double album publicly — after being approached by paparazzi late last month and asked how he'd "rate" his "Taylor diss track" as compared to others, he questioned, "My diss track? Oh!" then laughed and replied, "I haven't really listened to that much of it, but I'm sure it's good."

While the Grammy winner doesn’t name-check Healy on TTPD, a number of songs on the record seem to reference the star, whom Swift dated for several months in the spring of 2023, nearly a decade after they first sparked romance rumors.

Healy's aunt Debbie Dedes previously said she didn't think the musician would be bothered by Swift's songs.

“She writes about all her relationships, doesn't she? I don't think it will come as a shock to him at all,” Dedes told The Daily Mail of her nephew. “He's very happy in his new relationship so I'm sure he will be focusing on that.”

Healy has been dating model and Instagram chef Gabbriette Bechtel since September 2023.

Swift initially met the "Happiness" singer in 2014 and enjoyed what Healy has called a "flirtation," but didn't publicly strike up a romance until years later. In 2022, Healy confirmed his band worked with her on her 10th studio album Midnights, though their work was never released. Then, in January 2023, she performed during a guest spot at a 1975 concert in London.

By May, Healy used a break from his own tour to enjoy Swift's Eras concert in Nashville. Throughout the month, the two were spotted out on date nights and working together at Electric Lady Studios.

But by June, Swift and Healy had broken up. "She had fun with him, but it was always casual," a source told PEOPLE. "They are no longer romantically involved."

"It was a good time and ran its course," another insider told PEOPLE last year.