The family has not offered comment on the offer.
The unemployed single mother gave birth to octuplets last month after already having six other children.
Suleman's Whittier home is also facing foreclosure.
Suleman said the hospital has told her she might not be able to get her children from the hospital. She told television host "Dr. Phil" that Kaiser officials have said they might not release the children until she proves she can take care of them.
MORE LOCAL HEADLINES FROM LOS ANGELES
SEND TIP || REPORT TYPO || TWEET @abc7 || WIDGET