Podolski has only 18 months left on his contract with the Bundesliga club and has not been able to agree terms with them so far on a new deal. If the two sides can't come to an agreement, it is likely that the German will seek a move outside the country.
Both the Daily Mail and the Daily Mirror are now claiming that Arsenal are readying a £10 million bid for the player.
Podolski himself had told German paper Sport Bild back in mid-December that: "Moving to another club within the Bundesliga is something I can hardly imagine. If I decide to leave Koln, it will be to move abroad."
Arsenal have been very dependent on Robin van Persie for goals this season and with both Gervinho and Marouane Chamakh heading off for the African Cup of Nations, the Gunners are in desperate need of reinforcements.
Manager Arsene Wenger has already moved to try and sign club legend Thierry Henry on a two-month loan deal, but how much a 34-year-old Henry can help his former side is open to question.
Podolski, on the other hand, has been in superb form this season and is third in the Bundesliga scoring charts with 14 goals in 16 games.
German teammate Per Mertesacker, who moved to the Emirates in August, endorsed Podolski a few days ago, saying: "He is a powerful, great player, especially for the national team.
"He has scored a lot of goals, is a good striker with a very good finish. His left foot is unbelievable and I am a fan of him."
Despite the rumours though, it would be wise to keep in mind that Wenger is not a big fan of splashing the cash - especially during the January transfer window. His last high-profile winter signing was Andrei Arshavin back in 2009.