Following a slow start, Giovinazzi was able to gather momentum to match and beat Raikkonen on occasion further into the season. However, he lost the qualifying head-to-head 12-8 and scored fewer points compared to the Finn.
With Charles Leclerc secured to Ferrari on a long-term deal, the future of Sebastian Vettel at the Scuderia outfit beyond 2020 is unknown - and Giovinazzi views himself as a candidate to fill the potentially vacant seat.
"I would be lying if I said I do not dream of Ferrari," Giovinazzi told La Gazzetta dello Sport. "The most important thing for me is to fully concentrate on my work, but I know that if I perform well in 2020, I will have a chance.
"I already have a great relationship with Charles. We talk a lot and go to the same restaurants in Monaco."
Giovinazzi defended his maiden season, asserting that it was not easy to return to the cockpit of a race car after two years on the sidelines.
In 2017, he made two F1 race starts with Sauber and an appearance at the 2018 24 Hours of Le Mans, before he signed with Alfa Romeo full-time in 2019.
"I challenge anyone in any job to sit out for two years and come back," Giovinazzi said. "But in terms of speed, I was not far from Kimi. I was missing the racing, the starts, the strategies, the pitstops and how to manage the tyres.
"It wasn't like I returned to Formula 2, but to the highest level where I only did a race and a half against the strongest drivers in the world."
Looking ahead to his sophomore year in F1, Giovinazzi states that his primary goal is to get the better of teammate Raikkonen across the season.
"Beating Kimi is one of my goals for this season, but not the only one. It will be a crucial season, but it's always like that when there is a confirmation or a promotion," he said.
"He [Raikkonen] doesn't say much, and at first he did not help me because his results were better and it seems like there was a big gap. But he was an important benchmark for me to grow up in a professional way."
Bahrain International Circuit - Winter testing