A 3-0 reverse at Juventus on Sunday left Roma eight points adrift of Antonio Conte's men at the top of Serie A.
Prior to the match at Juventus Stadium, in which Daniele De Rossi and Leandro Castan were sent off, the capital club's last defeat had come in the 2012-13 Coppa Italia final against Lazio in May, two and a half weeks before Garcia was appointed coach at the Stadio Olimpico.
Despite enjoying a 17-match unbeaten run before losing to Juventus, Roma head into the last-16 tie against Sampdoria having won just two of their last eight fixtures.
However, Garcia's side can take confidence from a 2-0 victory at Sampdoria earlier this season, secured courtesy of goals from Mehdi Benatia and Gervinho.
While Roma were runners-up in the Coppa Italia last season, Samp suffered a third-round defeat to Serie B outfit Juve Stabia, losing on penalties following a 1-1 draw at Stadio Comunale Romeo Menti.
Roma have yet to play in the competition this term, while Sinisa Mihajlovic's men have recorded home wins over Benevento and Verona.
In the week's other fourth-round ties, Inter travel to Udinese and Fiorentina host Chievo.
Inter, winners of the competition four times in the last nine seasons, sit sixth in Serie A and recorded a 3-0 league win in Udine on November 3.
Both sides were beaten on their return to action after the winter break, Inter going down 1-0 at Lazio and Udinese falling to a 3-1 defeat against visiting Verona.
Fiorentina will be strong favourites to book a place in the last eight by beating Chievo at home on Wednesday.
The Stadio Artemio Franchi outfit are fourth in the league, having won their last four matches in all competitions.
Chievo, by contrast, are without a win in three and occupy 16th position in Italy's top flight.
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