Immobile is co-owned between both clubs and there are suggestions that he could make a January switch to Turin.
"I know that I am being talked about in the transfer market," he said.
"However, I spoke with President Enrico Preziosi before Christmas and he told me that I would be staying at Genoa.
"Juve? It would be nice to go there because I would be fighting for the Scudetto and not Serie A safety "