Horses from the Onaqui Herd near Dugway, Utah. © Bureau of Land Management
It is understood the search is centred on northern Nevada, the state which is home to about half of the 33,000 wild horses still roaming the rangelands of the 10 western states.
Mrs Pickens aims to set up a refuge for the more than 30,000 wild horses which have been taken from the rangelands by the Bureau of Land Management as part of its herd management strategy.
The horses are offered for adoption, but some of the animals are not wanted and adoption numbers have fallen as economic troubles in the United States have deepened.
The cost of keeping and feeding the horses is overwhelming the budget allocated for the maintenance of the wild herds and the bureau signalled it would look at the possibility of euthanizing some horses or selling them "without limitation" - a move which would see many go for slaughter.
Mrs Pickens' offer was disclosed on Monday at a meeting of the Wild Horse and Burro Advisory Board in Nevada.
Bureau officials have said publicly they welcome the offer by Mrs Pickens.
It is understood animals released into the refuge will be sterilised and it is hoped it will be able to take some or all of the animals taken by the bureau from the rangelands each year.
The bureau has a target herd size of 27,000 for the wild - some 6000 fewer than are currently estimated to graze the open country.
A foundation will be set up to support the refuge and it is likely arrangements will be put in place to allow the public to see the horses.
Meanwhile, the bureau has decided against euthanizing any captive horses for now, pending further developments.
It is believed another unnamed benefactor has offered to take up to 5000 horses.