The Azulones have gone nine Primera Division games without a win, their last victory coming at the end of Novembe, against Levante.
That torrid run has seen Getafe slip to 16th in the table, just four points above the relegation zone, and the fans have not hidden their discontent at the team's plight, chanting for Garcia to be sacked after the 3-0 defeat to Real Madrid last weekend.
However, the coach insisted he was not worried about his future at the club.
"The board have told me to keep working, encouraged us to stay strong and reminded us that there is nothing else to do but straighten out the situation and work hard," Garcia told a press conference.
"I haven't been given any ultimatum or assured I'm going to stay on, they just told me to prepare for the game (with Celta).
"Instead of talking about it, we need to act and get a good result."
Getafe face a Celta team who not long ago were in a similar situation to the Madrid side, but Luis Enrique's team have strung together three wins and a draw in their last four matches, propelling them up to 11th in the table, eight points above the relegation zone.
Yet the coach insisted his team were just as desperate for the three points on Saturday as their opponents.
"We are convinced beyond doubt that these three points are vital, because there's no team below us in the table that needs the points more than us," Enrique said.
"If we were to start relaxing now we would be making a terrible error."
Midfielder Mario Bermejo is Celta's only absentee, while Garcia has dropped Adrian Colunga and Michel from his squad.