The song that you speak..

If every note is a pitch, so is the word you speak or even the different syllables in the word you speak. Every voice has a natural scale. Depending on moods and expressions it may change. For example, when you are excited u might talk at a higher scale( Its not just a higher note cause all your variations now are with respect to that higher pitch hence it is a scale). So essentially you may say a sentence you speak is a collection of pitches which correspond to some note in some octave. Hence talking expressively is close to singing.

You can actually note down every syllable and its pitch when you speak. Your normal tone might even follow a pattern. :) Major/Minor? A particular ragam? - maybe an overkill ;) The possibilities are endless when you actually think of it this way :)

Singing is just more intellectual speaking. In speaking, you don't care what pitch it is but in singing you need to tune yourself to the specific pitch of the scale first and then produce a sound at the different pitch of the tune. This is as simple as it can get.
There are people who hum along with songs. Some understand tuning to the scale and some understand just the notes of the tune. The knowledge of how to tune, how to lower and higher your voice pitch is all that takes to start singing. Of course after that comes gliding of notes, gamaka for classical and practice. So its never too late to start learning to sing as its just an extension of what you are doing already :)