The Serie A outfit are looking to bolster their attacking options and have set their sights on the Germany international
The Stadio Olimpico outfit are keen to add some more firepower upfront and head coach Edy Reja reportedly considers Podolski to be the perfect addition to his squad.
The Germany international has a contract until the summer of 2013 with his current club, but he recently stated that he could leave Koln for sporting or financial reasons.
The forward is a product of Koln's youth academy and has spent his entire career at the Bundesliga club, aside from an unsuccessful three-year spell at Bayern Munich from 2006 until 2009.
Nevertheless, another move could be on the horizon as he has attracted the interest of several big sides with his good performances.
Podolski has been impressive in the 2011-12 campaign and has already scored nine goals this season.