According to Marca, both deals are done pending medicals and official announcements.
29-year-old midfielder Battaglia will join from Sporting CP where he has spent the last three seasons.
The Argentine will arrive on loan until the end of the season, with Alavés having an option to buy.
The Brazilian forward is no stranger to Alavés, having spent the 2016-17 season on loan there (37 appearances, seven goals).
Deyverson will also arrive on a loan deal and has already travelled to Álava to complete the formalities.
Alaves finished the 2019-20 season in 16th place, just three points above the La Liga relegation zone.
With Pablo Machin now in charge and several new arrivals, the Basque club will hope to do better in the coming season.