The 31-year-old is expected to move on in January given that he hasn't played for the Viola so far this term.
"At the minute I am not aware that Genoa are interested in Marchionni," agent Bruno Carpeggiani is quoted as saying.
"I know Rossoblu sporting director Stefano Capozucca personally and I have done for quite some time.
"I actually saw him recently in Cesena, but we never spoke about my client.
"We'll see what the situation is like in January where we will try to decide what is the best solution for the player and Fiorentina."