Media reports emerging on Friday had suggested that David Moyes had turned his attentions to the Italy international as he desperately tries to bolster his midfield ranks.
The Old Trafford boss has already seen moves for Thiago Alcantara, Cesc Fabregas and Marouane Fellaini fail in the transfer window.
A bid thought to be in the region of £10million was reportedly lodged, but Garcia has revealed that De Rossi is going nowhere, having rejected Manchester City to sign a new deal at the Stadio Olimpico in January.
"Daniele de Rossi isn't only a big player, but he's also a big man," the Frenchman said.
"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, who failed to score in 25 Serie A outings last season, started the new term in stunning form, netting a long-range effort as Roma beat Livorno 2-0 last week.
