updated 09/10/2010 AT 5:00 PM ET
•originally published 09/10/2010 AT 5:25 PM ET
Call it puppy love.
“Harry has been to Jen’s Beverly Hills house and they have had several restaurant dates as well,” a source tells PEOPLE. “Just like Jen, Harry is a dog lover and they both love the beach.”
Aniston, 41, and Morton, 29, the Pink Taco restaurant chain founder and Hard Rock heir who dated Lohan for about three months in 2006, have been stepping out together for about a month now.
“It still seems to be casual,” says the source, “but Jen has been glowing lately and seems very happy.”
Aniston also was spotted recently with Cougar Town actor Josh Hopkins – the actress shot a guest spot on the show – but pals are keeping a close eye on Morton.
“Jen and Harry used to be neighbors in Malibu,” a source tells PEOPLE. “Jen likes Harry because he is kind and low-key. Even though Harry is very successful and wealthy, he is not flashy and just like Jen, has a circle of close friends that are protective of him.”