The 28-year-old model and Bradley, 48, have been seen together several times over recent weeks, and she's enjoyed the experience of dating the Hollywood star.
"She loves that Bradley is a dad, because he gets it. She finds him more mature than guys she dated in the past. They keep spending a lot of time together. They have dinner dates several times a week. It makes her happy," a source told People, reports aceshowbiz.com.
Despite this, Hadid, who has Khai, three, with Zayn Malik, is determined that her daughter will be her number one priority.
The source said: "Her daughter will always come first."
In October, a source claimed that Bradley felt "excited" about getting to know the model. The actor loves spending time with Gigi and she is "exactly his type."
The source told DailyMail.com: "Bradley is excited about getting to know Gigi. He hasn't felt this excitement about a woman in a very long time. They are taking it slow, but he's very into her. She is exactly his type."
Bradley and Gigi were said to be "having fun" together, in spite of their 20-year age gap. A second source said: "Bradley is eager to date again and be in a relationship.
He loves all that comes with it and Gigi is beautiful and she gets it, she is really cool and knows her way around relationships like this with famous men, so they are both having fun."
The insider also acknowledged that their rumoured romance could "turn into something serious."
The source shared: "They are seeing how it all goes, it is still really new, but there is no disappointment with what has been happening so far. It is all looking very positive to turn into something serious."