TMZ has confirmed the married couple is expecting, though it's unclear how far along Kat might be at the moment. Reports surfaced last year that they were eager to get their family started as soon as possible -- they got hitched just last June after about a year of dating.

No word yet on whether the kid might be a girl or boy, but it looks like the mom-to-be has a baby bump well underway right now ... she was spotted out this week in L.A. with her mom, Maria Shriver, with loose clothing and a hoodie on, which seems to show her belly's grown. Per our sources, Kat instantly covered up when she saw she was being photographed. The couple hasn't made the announcement yet, but we know it's true. People broke the news.

This would make baby no. 1 for Kat, but it'd be Chris' second child. He's got a young son, Jack, that he shares with his ex-wife, Anna Faris ... to whom he was married for several years before getting divorced in 2018.

They both moved on -- Anna appears to be engaged. Interestingly enough, we'd heard Chris didn't want more kids in the foreseeable future, and that issue was one of the sticking points at the end of CP and AF's marriage.

In any case, the new baby means a lot for the Schwarzenegger family -- specifically, Arnie himself. This would be his first grandkid EVER, which is wild ... 'cause all of his own children are pretty damn grown now, but just haven't planted a seed. 'Til now, that is.