The Grammy winner has also reportedly been renting a house in North London while spending time with Alwyn, adds the outlet.
Last year, Alwyn had a breakthrough role in Ang Lee’s war film, Billy Lynn’s Long Halftime Walk. “It’s really nice to have people excited about … me,” he told PEOPLE about getting attention for the role. “But it’s hard to get caught up in that. Maybe it’s just my nature. I just want to take things a day at a time.”
Alwyn also recently wrapped his latest film, The Favourite, starring Emma Stone (one of Swift’s oldest friends).
The “Shake It Off” singer was last romantically linked to Tom Hiddleston. After a high-profile months-long romance, the stars called it quits last September.
This article originally appeared on PEOPLE