Well, be careful about trying to effect too much of a change with exercises. You are born with the voice you've got, and, aside from some hormonal changes, not much will affect your basic capable range. That being said, there are often things we do when we speak that affect our speaking pitch. Tight laryngeal (throat) muscles and lack of low breath pressure (speaking from high up in your chest - or speaking in your throat) can artificially "squeeze" your sound, making it thinner than it might be naturally.
Some things to try. Lie on your back (on a firm surface), if you can do that safely, and focus on your breathing. Breathe in your nose and out your mouth. With your lips together and lots of space in the back of your throat (like there's a virtual globe of fruit back there), hum. Start with a medium-high note for you and smear or slide the pitch, like a siren, slowly and gently down to the bottom of your range and gently back up as high as you can go comfortably. Repeat a few times. This can help you relax your breathing and vocal mechanisms. In this relaxed state, try speaking some gentle words, but use more air to make the words than you might normally use. Be conscious that speaking uses up air. (stop if you get light headed). Making sure you're using air should give you a better sense of what your voice might be capable of. Try taking medium sized breaths (no need to tank up), and use up all your air speaking the sentence. Try this sample "...When the sunlight strikes raindrops in the air, they act as a prism and form a rainbow. The rainbow is a division of white light into many beautiful colors..... As an aside, NOT using enough air when we speak has the automatic effect of causing us to conserve air by restricting it - usually in the throat. That makes the voice sound tight and constrained. Sometimes even higher in pitch.
If you want to get a better idea of what might be possible with your voice, I would highly recommend a classical voice teacher (get a referral from a university voice program if possible - just email them - most schools are happy to point interested people in the right direction). If you're particularly concerned about how your voice sounds, a speech language pathologist (don't be scared - they're awesome!!) can help you with specific exercises tailored to your specific instrument. Young schoolteachers often have hoarse and scratchy high sounding voices after their first year of teaching (sounding like they were in the bar or club all night, yelling). They and others can benefit greatly by learning how to use the voice efficiently and safely.