A deed can certainly be prepared and filed with the proper county government agency, transferring property from one person to another (or to a business entity).
But it is not typical for a piece of real estate property to be transferred to a grantee (in this case, the mortgage holder of the property who has not foreclosed and won’t return the investor’s phone calls) without that person or entity’s consent.
So while the deed could certainly be prepared and/or filed, the grantee may object to such a transfer — and may even seek to transfer it back to you.
Further, the transfer of the property to the note holder would most likely not remove or eliminate the financial obligations arising under the loan or note for said property.
So merely transferring the property would not eliminate the obligation to pay the amount borrowed and secured by the mortgage.