Ferrari academy graduate Giovinazzi is nearing the end of his second season with the Italian team but he is racing under increasing speculation he could be replaced for next season by current F2 championship leader Schumacher.
Across the opening 10 races of this season, Giovinazzi has only managed to finish ahead of veteran team-mate Kimi Raikkonen in the classification on three occasions, and just twice when both men have reached the chequered flag.
Ahead of this weekend's Eifel Grand Prix, in which Giovinazzi will be replaced by Schumacher in FP1, he and Raikkonen have each scored two points from ninth-place finishes in the season-opening Austrian and Tuscan Grands Prix respectively.
Giovinazzi, though, has no issues with his level of performance. He said: "I’m happy with what I have done so far.
"I just need to keep pushing hard and see what happens. I think there is still a lot of the season [remaining]. Of course, I just try to do my best and see after what will happen."
Giovinazzi believes a more competitive car this season would have been of benefit to his cause.
"We want to improve our car in all areas," added Giovinazzi. "This is what we are doing.
"We can’t find tenths [of a second] really easy but we are doing our job and I think the car is improving, especially since the first race.
"We just need to work like that and then try to be a little bit closer to the midfield. We are fighting with the Williams and Haas, and our next target is AlphaTauri that is now much in front of us. We need to be closer to them."