No, if you are paying interest to an individual, you need their Social Security number or EIN.
If they don't want to give you their social security number, have them get a EIN.
Home mortgage interest is only deductible if you Itemize deductions. It the Standard deduction is more, the interest won't matter on the Federal return.
https://www.irs.gov/businesses/small-businesses-self-employed/apply-for-an-employer-identification-n...