Financial institutions are required to send you a 1099-INT form if you have earned more than $10 in interest during the tax year. If you earn less than $10 during the tax year they may still send you a 1099, they're just not required to, and it sounds like if you're getting 10 cents a month you're earning less than $10/ year. BUT, even if you don't receive a 1099 you are still supposed to report it as any & all interest earnings are taxable.
To me, the more important question is why in the world are you keeping $10k in savings with Bank of America and Wells Fargo when they pay you so little interest??? The big banks are the worst at paying such low interest on savings. Good, solid financial firms such as American Express & Discover and many more are currently paying 2.10% interest on savings - for $10k that's $210 per year, $17.50 per month. Bank of America and Wells Fargo are cheating you paying such low interest.
Here are current savings rates at Bankrate.com:
