According to the Rome-based newspaper, Corriere dello Sport , Robben has always been a favourite of the Juventus head coach Antonio Conte, who was even more impressed after the Champions League quarter-final that saw Bayern beat Juve 4-0 on aggregate.
A move for the 29-year-old is looking more plausible now that Bayern Munich have announced the capture of Borussia Dortmund playmaker Mario Gotze.
The Corriere dello Sport claims the Germans would be willing to release the Dutch international for around 18 million euro.
Robben would fit the bill of 'top player' that Juventus are looking for and provide more width for tactical experimentation.
Bayern Munich are practically in the Champions League final after thrashing Barcelona 4-0 in the first leg of their semifinal Tuesday.
Meanwhile, Germany's under-21 midfielder Sebastian Rode will move from Eintracht Frankfurt to Bayern Munich, said a senior official of the Frankfurt club.
Frankfurt CEO Heribert Bruchhagen Thursday said Rode will leave either at the end of the season or when his contract expires in 2014.
Just two days ago, Bayern recruited another young midfielder Mario Goetze from Borussia Dortmund, who will join the Bavarians in July.
Bruchhagen said money is the key element that Rode and other young talents chose to join Bayern.
"They can earn four times as much money at Bayern as they can here," he said in an interview with German daily Bild. "End of story. The budget at Eintracht is 30 million euros, it's 150 million at Bayern."
With six rounds left, Bayern Munich have made sure of winning Bundesliga while they are also bidding to become the first German team to win the treble of European, cup and league titles.