The Iceland international is on the radar of Tottenham ahead of the January market.
He told the Telegraph: "I really want to test myself at the highest possible level. Since I was a child I have always dreamed of playing in Premier League, it's something I want to try."
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In the meantime, Gudmundsson added: "Let's see what happens at the end of the season.
"At the moment I have a contract with Genoa (until 2027) and I'm fine. I'm very happy with my season with the Rossobl in Serie A: I have some decent qualities such as good finishing, good passing, good set pieces."