I don't know much about the N. American monsoon, but Emily has a great blog post on it here:  https://www.climate.gov/news-features/blogs/enso/north-american-monsoon

The seasonal precipitation outlook is available here (updated once monthly):  https://www.cpc.ncep.noaa.gov/products/predictions/long_range/seasonal.php?lead=1

For this summer at least there is some tilt in the odds toward wetter conditions for parts of southern Arizona.  It's not a particularly high probability forecast though.