Contact the lender to see if the mortgage is assumable. Better yet, if you can find the original mortgage documents your parents signed, read them. All FHA mortgages written up to the mid-1980s were freely assumable - no lender approval required. All VA mortgages were freely assumable by another veteran with VA eligibility, no lender approval required. Those mortgages are all long gone - either discharged early by a sale or completely paid off.
Most mortgages today are not assumable, period, but some may be, with the lender requiring that the prospective buyer pass the lender's income and credit worthiness tests. This is your only hope of getting that mortgage into your name; your parents cannot just sign it over to you. They can sell the house to you and you can go out and get your own financing. Or they can leave it to you in their estate when they are gone, and if a mortgage still exists at that time, you may take it over under a special provision of the law ( in the Garn-St Germain Act).