The German forward has been a peripheral figure at the Emirates Stadium this term and has regularly been linked with a move away, most recently to Serie A club Inter.
Podolski has regularly voiced his desire to play more regularly under Arsene Wenger, although the Frenchman insists the striker remains part of his plans.
The former Bayern Munich man has been suffering with a groin injury and took to Twitter to dismiss allegations he stormed out of the club's Hertfordshire training complex.
He wrote: "I try not to comment on stories I see in the papers but when I see something that questions my commitment & love for the club then I must speak up!
"Here 'The Mirror' have tried to make a story out of nothing. I find it incredible that newspapers are allowed to print pure lies to get people's attention.
"In order to 'storm' off the pitch you have to actually be on the pitch in the first place, I spent the whole session inside with medical staff. It seems it is 'The Mirror' who stormed to the keyboard too quickly.
"Nevertheless I wish 'The Mirror' a Happy New Year and more luck with correct headlines in the future."
Podolski, 29, has often been linked with a return to first club Cologne, while Inter coach Roberto Mancini was quoted recently as saying the striker was on their list of targets in January.
However, Wenger dismissed the Inter link this week by stating the rumours were a "joke".
"That is a joke. Inter Milan is not serious. It is nothing serious," he told a news conference.
Wenger also played down the prospect of Podolski leaving the club on loan, stating a temporary move was more appropriate for younger members of the squad.
