Reports have claimed that the Red Devils have lodged a £10m bid for the Italian international central midfielder, who has played exclusively for Roma since turning professional in 2001.
Garcia is adamant, though, that De Rossi will remain with the Giallorossi even if David Moyes tries to lure him to Old Trafford before the 11pm deadline on September 2.
"Daniele De Rossi isn't only a big player, but he's also a big man," Garcia told a press conference. "He has been here at Roma for a long time and he wants to play with this jersey.
"We spoke when he came back from his holidays and we said that, if it got past a certain date, he would certainly remain with us.
"He will stay here for the whole season and this is something that satisfies me a lot."
De Rossi has made 307 times for the Stadio Olimpico outfit, scoring 34 times in the process.