The 27-year-old singer was introduced to the Florence and the Machine guitarist through mutual friends Robert Pattinson and Kristen Stewart, reported Contactmusic.
The couple was first spotted together at California festival Coachella earlier this month, and was recently seen enjoying dinner at Hollywood's exclusive Chateau Marmont hotel with Perry's friends.
"Rob had his arm around Katy while the group were chatting. He looked very at ease. It's early days but she's confident it may be going somewhere," a source said. PTI CORR AYM