Arsenal, Manchester United and Chelsea will now face a tough task of snapping up the Colombian midfielder this summer.
The three Premier League giants have been linked to the 27-year-old, but his father is keen for him to continue his career in Italy.
According to Calcio Mercato, he said: "He [James] has received many offers.
"Juventus? He is a good friend of Cristiano Ronaldo. The way I see Italian football, going to Juventus would be a good decision."
Ronaldo and Rodriguez became good friends during their time together at Real Madrid.
And it was reported earlier this month that Ronaldo called Rodriguez to convince him to join him in Turin.
The 27-year-old has entered the final stages of his two-year loan deal with the German side from Real Madrid.
Bayern have an option to make the move permanent for £39.5 million, but he has failed to live up to expectations this term.
He has made just six starts for Niko Kovac's side this season and does not look set to extend his stay.
James Rodriguez's stats in the Bundesliga this season
Minutes played: 576
Chances created: 20
But when asked about his future beyond the summer, he said: "That's still four months away. Currently, I only think about Bayern."
Rodriguez's dad confirmed Arsenal's interest in a loan move last month, but admitted he is comfortable in Germany.
He said: "He is comfortable in Munch. I don't have news about it, but there may be offers based on those rumours coming from England.
"He is calm and he feels that he's at a good level again and that he's physically strong."
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