People magazine Wednesday quoted a source close to the singer as saying: "She's happy to have a house that's hers."
Simpson and Lachey are having their divorce handled privately by a Los Angeles judge to keep the details of their split private.
"There is no squabble, and we are hoping for a quick and private procedure," a source from the Lachey camp told People.
The source said Lachey was not surprised when his wife filed the divorce papers.
"He was hoping for the best, but as time went by he was prepared for what became inevitable," said the source.