AS Roma's plan comes after Juventus, currently top of Serie A, became the first top Italian club to own its own ground having built a 41,000-seat stadium instead of relying on the Stadio delle Alpi which it had to share with Torino.
Such purpose-built modern facilities could help Italy in any future bid to host either a World Cup or European Championship.
"It's been a long process but from the new ownership point of view we've been working on it for the last year. It shows our belief in Italy and the Italian economy," Roma President James Pallotta said in a comment.
Italy's ageing stadiums have the second-lowest attendance among the "big five" European football leagues, with the English Premier League and Germany's Bundesliga out in front.
"The fact that a stadium will be built thanks to the efforts of American ownership is a powerful message for the marketing of our city," Alemanno said.
It was not clear how much the stadium would cost, but Claudio Fenucci, part of AS Roma's management team, said: "For every new stadium the cost of each seat is about 3,000 to 3,500 euros."
