The German forward is reportedly set to leave the Italian side this summer and has a number of potential suitors, but both Ligue 1 side Monaco and Liverpool are thought to be chief among them.
Indeed, it seems Monaco are keen to know whether a deal is going to happen sooner rather than later, with La Nazione claiming that they have set a deadline for him to make a decision on his future, thought to be Tuesday.
That potential deadline could see Liverpool forced into a move earlier than they probably would have expected. The Reds are keen to add firepower to their side after their forwards struggled so badly last season, and the 30-year-old would be suitable given his goalscoring pedigree.
Sell before you buy
However, much of course remains on the futures of those forwards currently at the club, who manager Brendan Rodgers may have to sell first before he can recruit further.
Mario Balotelli is likely to be one of the first names on the for sale list after his first and disappointing campaign, but the Reds are unlikely to recoup what they paid for him.
The same can be said for both Fabio Borini and Rickie Lambert, although like Balotelli, there is sure to be interest in Borini from Italy. Lambert is sure to stay in England, but it is isn't clear where.