I am going to respectfully differ with attorney Chen in an answer to this question.

The California Judges Benchbook on SEARCH AND SEIZURE lists a number of factors that must be considered in terms of EXPECTATION OF PRIVACY:
1. Does the defendant have a property or possessory interest in the place searched or items seized?
2. Does the defendant have a right to exclude others from the place searched?
3. Does the defendant have a subjective expectation of privacy?
4.. Has the defendant taken normal precautions to maintain privacy?
5. Was defendant legitimately on the premises.

Item 1. has a continuum between very legitimate people on premises to do a contracted job(babysitting) and people who are there illegally. Much would seem to revolve around whether the person who is there, took possession under some color of right of someone else quthorized to grant permission for them to be there.

Thus the term "squatter" does not describe the conditions as to how the persons squatting first came to be on the premises. If they are trespassers with no colorable claim of right, then item 1 would seem to fail.

Further, keep in mind that searches deal with places and things. As to the place, it is clear that an owner can give permission to search the place, even after the fact, so "no colorable right squatter" loses when the owner gives permission to search. As to "things", the squatter may have the same rights as someone sitting on a park bench, however if the owner is given permission to search and eject trespassers, a search of the trespasser (squatter's) goods is sure to follow, either incident to an arrest for trespassing or a Terry-type search or a safety sweep.

Of the factors left, a raw (no colorable right) squatter would not seem to be able to identify others he could eject (except for some adverse possession against the homeowner) and to qualify as starting the adverse possession time period, the possession is normally required to be OPEN AND NOTORIOUS.

As to 3, can a defendant as trespasser have a right to privacy as to premises that he, for example, broke and entered? Upon which he has no key?

How has the squatter acted to maintain his privacy under 4.?

How can a "squatter" be legitimately on the premises under 5?

Now, this would all change if the "squatter" was a holdover tenant. His initial tenancy would give him rights in the property until eviction, and elements 2,3,4 would seem to be satisfied in this case also. He might even qualify for 5 absent eviction.

So, the real question to ask is "how did the """squatters""" come to be on the premises?????

If trespassing, the contact with the trespassers can supply a lot of the probable cause to search.

The facts and circumstances relating to all 5 (and other) factors need to be addressed.

Meanwhile, who wants to take a chance? If there is anything of concern, WHY KEEP IT ON SQUATTER PREMISES???????

WHY TAKE A CHANCE?

Further, if the premises were entered illegally, a burglary charge might be possible as well.

I suggest that you consult with a lawyer personally and give him all the facts.

Lastly, what is a "squatter"? Here is the dictionary view: (A) An individual who settles on the land of another person without any legal authority to do so, or without acquiring a legal title.
In the past, the term squatter specifically applied to an individual who settled on public land. Currently it is used interchangeably with (B) intruder and (C) trespasser.
So "squatter" typically means someone coming onto the premises much like a trespassing burglar.

A "holdover tenant" is another matter.

Hire an attorney and give him all the facts, and get a better answer.

The fact that the property is bank owned, the fact that the property is currently on the market, and the fact that the house has been vacant for 4 months makes no difference in the rules that apply for searches and search warrants.