The two have been trying to keep their relationship under wraps. Pattinson, 27, who recently ended an on-and-off relationship with Kristen Stewart, is enjoying getting to know Elvis Presley's granddaughter.
"Rob and Riley are having a really great time together, even though it's very early. There is an attraction to each other. They just get each other," femalefirst.co.uk quoted a source as saying.
"Rob thinks Riley has a cool level head and is not impressed by stardom at all. Rob just loves that about her," the source added. The couple also enjoy spending time at Pattinson's house and are involved in doing typical stuff.
"He loves that she'll go into his kitchen for like 10 minutes and come back with a delicious plate of pasta. They just do typical stuff that has pretty much started all his relationships. They get into debates about politics, human rights, things they had read in the papers that morning.
"She's pretty good on the piano and he'll often pull out his guitar and they'll have a mini jam session, making up silly songs and funny limericks," said the source.
Pics: Prabhas, Tamannaah Bhatia at 'Baahubali 2' first look launch at MAMI
'Ae Dil Hai Mushkil' photos: Aishwarya, Anushka, Karan get candid at MAMI
Photos: Huma Qureshi, Neha Dhupia and other celebs at MAMI
Photos: Amy Jackson, Daisy Shah at Mumbai airport
Photos: Sridevi, Irrfan and other celebs at 'Mughal-e-Azam' screening