According to American tabloid National Enquirer, the 'Can't Be Tamed' singer first rang Patrick Schwarzenegger after asking her friend Selena Gomez for his number.
A source claimed that the pair have subsequently shared "several coffee dates" and that Cyrus is "looking to rope Patrick into a full-fledged romance".
However, Patrick's parents - former governor of California Arnold Schwarzenegger and journalist and author Maria Shriver - are rumoured to be dubious about the relationship, worrying that "Miley might lure Patrick into the Hollywood party scene".
Reports last month suggested that Cyrus was dating former boyfriend Liam Hemsworth again after she hinted that she was not single. Meanwhile, Patrick's parents released a statement earlier this week announcing that they are separating.
In contrast, Cyrus's own parents, Billy Ray and Tish Cyrus, have reconciled.
Watch a video of Miley Cyrus covering Nirvana's 'Smells Like Teen Spirit' at a recent concert in Ecuador below: