Brentford boss Mark Warburton plans to take another look at Tommy Smith before making a decision on his future.
Everton have been forced to wait to finalise the signature of Chelsea striker Romelu Lukaku.
Podolski, who joined Arsenal from Cologne last summer, is thought to be attracting interest from Turkish giants Galatasaray.
However, Podolski, who is currently away on international duty with Germany says he is happy at Arsenal and has no intention to leave the Emirates.
"I feel very comfortable and I am completely satisfied with my first year in England," Podolski told Spox.com.
"I have no intention to leave the club.
"Rumours are rumours and I cannot stop them."
Podolski scored 16 goals for Arsenal in all competitions in his debut season to help them finish in fourth spot in the Premier League.