The Frenchman's position has come under fire following Roma's disappointing performances in recent months and reports from Italy suggested the club are already lining up potential successors.
Capello was believed to be one of the candidates to take Garcia's place, but the 69-year-old has ruled out a return to the Stadio Olimpico as he does not want to taint the memory of his previous spell in charge, when he guided Roma to the Serie A title in 2000-01.
"There is no way I will return to Roma," Capello told Omnisport.
"I have good memories of my time in charge of Roma and I want the people to remember me for the Scudetto that we won. I wish Roma all the best, though.
"Garcia did well the past two seasons, but is having some problems now. That can happen to any coach. You go through good moments and bad ones.
"We have to accept that and try to understand the reason behind the problems. It could be due to injuries or because of players who are not in great form for different reasons."
Roma have dropped to fifth place in the Serie A table following their recent struggles, are on a seven-game winless streak in all competitions and were dumped out of the Coppa Italia on penalties at home against second-tier Spezia on Wednesday.