Spalletti, 56, reportedly signed a contract until 2017 in Miami in a meeting with club president James Pallotta and his staff in the US.
Garcia reportedly had to go in his third season after Roma managed only one win from the last seven games and have slipped to fifth place in the Serie A at the halfway mark of the season.
Roma are yet to make an official announcement on Garcia’s fate or a possible signing of Spalletti.
Spalletti’s first term at the club was from 2005 until 2009. He led them to three runner-up finishes in the Serie A and two Champions League quarter-finals. He then coached Zenit St Petersburg to two Russian titles before being dismissed there in 2014.