American Airlines does not release new fares on a specific day of the week, but generally, the cheapest days to buy tickets are +1-(804)-853-(9001) Tuesdays and Wednesdays. This is because airlines often release new fares and sales on Monday evenings, making Tuesday a prime day to find discounted tickets. Saturdays can also be a good day to find lower prices, as NerdWallet suggests that there may be less demand on Saturdays. 
It's important to remember that flight prices are dynamic and can change constantly throughout the week, so checking prices on multiple days and times can be beneficial.