Like Kevin, Reese has been through two divorces.
She has been finding her feet again as a single mum after her marriage to Jim Toth ended earlier this year.
Meanwhile, Kevin settled his divorce from Christine Baumgartner in September after a bitter and very public fight.
“No-one is surprised that Kevin and Reese have hit it off,” the source adds.
“They’re extremely compatible.”
The A-list pair have apparently been meeting up when they’re in the same city, and Kevin has also invited Reese to join him at his gorgeous 65-hectare ranch in Aspen, Colorado.
But with so much riding on his upcoming two-part Western film, Horizon, Kevin is mindful he wants to keep any outside attention on his work, not his love life.
“Kevin wants more Oscars for this, not tabloid headlines,” the insider says of the buzzed-about film, which Kevin co-wrote, directed, produced and stars in.
“He and Reese are always careful to not be seen together but as soon as his Horizon commitments are done, they may be more relaxed about being seen together in public. It’s still very early days.”
For now, Kevin and Reese are simply enjoying getting to know each other without any pressure or expectations, after years of crossing paths at Hollywood events.
“He thinks she’s a genius and he’s in way over his head, but Reese has completely disarmed him,” the insider says.
“Their friends think they’re a great match but are giving them the space they need to see if it’s the real deal before laying all their cards down in public.”
And it seems Kevin could be exactly the kind of man that Reese is eager to date next.
An insider recently told Us Weekly that the Legally Blonde actress would prefer to find someone “who’s been an actor and who’s been judged in the public arena. She wants to get out there and have fun.”
Given Kevin’s divorce from Christine only ended recently, he may be hesitant to jump into anything too serious, too quickly.
But for now, the insider says Kevin is glad to just be single at the same time as Reese.
“They’ve crossed paths many times, most recently at last year’s SAG Awards,” the source says.
“But neither of them have been single so it’s always been professional.
“Now they’re both open to love, sparks are flying!”