Federer maintained his bid for a century of titles with a 6-3 3-6 6-3 win over Fernando Verdasco on Wednesday.
And he will face Hungarian Fucsovics, who is at a career high 35 in the world rankings.
“I know Marton quite well actually,” said Federer.
“He came to Zurich to train with me. He was nice enough to come there. I don’t remember how long we spent, but a few days practising together there. We had a great time. Then, I played him at the Australian Open last year. [It was a] good match… He’s improved.
“He likes the fast surfaces. He likes to play up in the court. He has the power when required. I think it’s going to be definitely a match that’s going to test me.”
15:00 Hello and welcome to coverage of Roger Federer’s quarter-final against Marton Fucsovics in the Dubai Tennis Championship.
The players will be on the court once Stefanos Tsitsipas and Hubert Hurkacz complete their match.