The Germany international, who is valued at 14 million euros by the Gunners, also has offers from the New York Red Bulls, Galatasaray, Wolfsburg and Olympiakos.
Juventus leads the race for Lukas Podolski after Arsene Wenger sanctioned the sale of the Arsenal forward, Goal UK reports, with the New York Red Bulls also in contention.
The German was told in a meeting with the Gunners boss that he can find a new club in the final week of the transfer window. The Gunners would prefer to sell the 29-year-old if their valuation of between 12.5 million euros and 14 million euros is met, rather than loan him out for the season.
Podolski has an agreement in principle with Italian champion Juve, but he also has offers on the table from Wolfsburg, Galatasaray, Olympiakos and the Red Bulls.
Podolski was a marginalized figure at Emirates Stadium last season and, with growing competition for the attacking roles, is willing to move in search of regular minutes.
He did not feature in the 18-man Arsenal squad that traveled to Everton on Saturday, even though he was fit to play.
Podolski, who turned 29 in June, has two years remaining on his contract and was ignored in the flurry of extended deals handed to senior players at the end of last season.
Wenger does not believe that the Germany international has the physical power and technical ability to spearhead the attack and he is behind the likes of Alexis Sanchez, Theo Walcott, Jack Wilshere, Santi Cazorla and Tomas Rosicky in the battle for the flank roles.
Podolski is believed to be the only senior Arsenal player who could be sold in the final weeks of the window. Wenger is keen to hang on to Costa Rica forward Joel Campbell, who has attracted strong interest from Premier League clubs and overseas.