The Italian capital club began their tour of the United States with a win on Wednesday, Marco Borriello's 90th minute strike earning a 1-0 triumph over Liverpool at Fenway Park.
Roma have already recruited extensively in the transfer window, bringing in winger Juan Iturbe from Verona, while also signing midfielder Seydou Keita and left-backs Ashley Cole and Urby Emanuelson.
Genoa centre-back Astori is a reported target for Roma after his prospective move to city rivals Lazio fell through.
And Garcia revealed that sporting director Walter Sabatini is working to try and bring a central defender to the Stadio Olimpico.
"We all know that we need another central defender," Garcia said.
"This is why I have brought many youngsters along to see if more than one can help us in the season.
"Sabatini is working on this and we need to find the right man to be even stronger this season.
"We will see later, but there is no rush to find this central defender, but if there is an exciting opportunity then we will take it."
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