The 55-year-old writer - who split from the 'Terminator' star earlier this year after it was revealed he fathered a boy named Joseph with his family's housekeeper Mildred Baena 13 years ago while they were still married - is looking to purchase the luxurious property in Los Angeles district Brentwood, which is just down the road from her former marital home.
According to gossip website TMZ, Maria - who has four children, Katherine, 21, Christina, 19, Patrick, 17, and Christopher, 13, with the former Californian governor - wants to be close to Arnold so it's easier for the custody arrangements of their two younger children.
Earlier this week, it was revealed Arnold, 63, is to give Maria a "very generous divorce settlement" and more than she is owed under Californian law.
An insider revealed: "Arnold realises he is to blame for the collapse of his marriage. Maria was a loving wife and mother, and he doesn't think that any amount of money can minimize what he has put her through. He wants to do the right thing, and go Above And Beyond what is required of him under the law.
"This is going to be a very amicable divorce, and it won't be played out in the media. Neither one of them wants that. Arnold hasn't lost his mind, he is going to be giving away his Fortune to her. He wants to show his children that he is taking responsibility for his actions."
Maria - who filed for divorce from Arnold last Friday (01.07.11) - is entitled to a 50/50 split of all the couple's assets accumulated during their marriage because California is a Community Property state.