The 30-year-old model and the 'American Sniper' star's relationship has never been better after news broke that Irina is reportedly expecting a child with Bradley.
A source said: ''Engagement or marriage may happen under the radar because they are very private people.
''They see themselves spending their lives together and building a family with more than one child. They are in an extremely happy place between the two of them.''
And Irina is said to be taking pregnancy very well but is ''more tired than usual'' with all the travelling she is doing.
An insider added to E! News: ''Irina is doing pretty well. She has some food cravings because she's pregnant. She is not the kind of woman to count calories, but she has been taking it easy. She's also exercising in moderation.
''She is more tired than usual. She has been travelling a lot and hasn't had time to see Bradley but plans on seeing him very soon. They are in communication a few times a day. They are really happy and can't wait to have their baby.''
Meanwhile, Irina recently revealed she is keen to have children sooner rather than later.
She shared: ''I think family is the reason why we are here. I love my job and it's very important to me. I really enjoy what I'm doing but it's not the most important thing in my life - family is, friends, people who I love. My father was married to my mother for more than 20 years and, yes, definitely one day I want to have a family because that is the most important thing on this earth.
''I don't think there is a perfect time. I think it's more important to have the right person by your side. My sister had her baby when she was 22, and for her that was the perfect time. I will be 31 in January, so maybe soon it will be my perfect time. I don't know - time will tell.''
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