Yes usually one can be made to fit. It depends mostly upon the fitting for the presser foot, whether it's a threadle, hand crank or electrial doesn't matter. Can you let us know model number or post a picture? If it's a general low shank they are easy to buy, and you can look out for a Swiss Zigzagger made for Singer machines.
I don't know older White machines well enough to point to a suitable walking foot, but adaptors are made for some models, and can be made if you know someone with access to a metal shop or the right tools. The only thing stopping us is really the cost of having stomething made, so we usually make something our self or look for someone who is willing to do it for the right price.
Last edited by Mickey2; 01-15-2017 at 02:37 PM.