The "Wrecking Ball" singer was photographed with the 21-year-old son of Maria Shriver and Arnold Schwarzenegger in Los Angeles on Halloween.
"They spent a lot of time together this past weekend," a source tells PEOPLE. "They have been hanging out at his L.A. apartment and at Miley's house."
And on Thursday, the two hit up Universal's Haunted Hayride, along with a group of friends.
However, a Cyrus source says the singer, who was previously engaged to actor Liam Hemsworth, insists she's not dating anyone at the moment.
But Schwarzenegger has had a crush on Cyrus, 21, for years, telling Details magazine in 2011: "My eye … is set on Miley."
They were rumored to have gone on a couple dates that year, before Cyrus ultimately got back together with Hemsworth.
Since ending her engagement, Cyrus, who recently wrapped up the Bangerz Tour with an Oct. 23 date in Perth, Australia, has been romantically linked to Twilight actor Kellan Lutz and Bangerz producer Mike Will Made It.