Having recently announced his decision to retire, 15-year F1 veteran Massa said that he would consider offers to race instead in DTM, WEC or Formula E in 2017.
Formula E boss Agag told Spain's El Confidencial: "When I heard he said that [about Formula E], I sent him a Whatsapp and told him we should meet.
"I'd love him to come here. In fact, it's the teams who choose their drivers, but I would love for someone with such quality to come to us.
"[Massa] also mentioned DTM and WEC but the fact that a driver like him says he wants to come to us means that we are a real alternative for the big boys."
More broadly, Agag has been linked with a role in F1 management, and not just because he is the Formula E equivalent of Bernie Ecclestone.
Formula E is co-owned by Liberty Global, a sister company to F1's new owner Liberty Media.
Asked if we will see him in the F1 paddock soon, Agag said: "I don't know.
"There are many rumours but there is nothing real and I have my moral responsibility to stay in Formula E. Let's see.
"I don't know what will happen because although Liberty Media and Liberty Global are different companies they have the same shareholders, but basically there have been no discussions."
Formula 1 continues next weekend in Malaysia.