A source close to the star told Us Weekly magazine: “She’s so into him. It’s relatively new. But they’re really cute together.”
The 31-year-old star is said to have enjoyed a romantic date with Alex at Katsuya in Los Angeles’ Encino and weren’t concerned about hiding their affection for one another.
The source added: “They were holding hands the whole night.”
Jennifer – whose ex-boyfriends include John Mayer, Ross McCall and Carson Daly – recently admitted she feels she is a better person when she is in a relationship.
She said: “I feel like as a person, I am better as a couple. But I am learning a lot about myself.”
The brunette beauty has also spoken about how much she enjoyed being single as it was a new experience for her.
She said: “My love life is just me, and I’m very happy about it. I’ve not done the single thing very much, as you know, and I’m happy to do it.”