The Mirror says City have made Podolski their next major target as they bid to turn the club into a Premier League superpower.
Podolski, 23, would still represent a major coup as he has smashed a staggering 30 goals in 56 matches.
He is far superior to Germany team-mate and Stuttgart striker Mario Gomez, who City tried to buy on Deadline Day, and admitted: "Everything is possible."
Podolski added: "I would be a bad footballer if I contented myself by sitting on the bench.
"I could tolerate it if it was a case of two or three weeks, but there comes a point when one has to draw the line and say: 'This is too much! I'm not making any progress here'."