While Old Trafford appears to be the preferred destination of the Dutchman, who announced earlier this summer he would not be signing a new contract, Manchester United will have to move closer towards the £20 million at which Arsenal appear willing to do business for a player who could walk away for nothing at the end of the campaign.
Gunners boss Arsene Wenger has signalled his intent for the challenges ahead by adding experience in the form of German striker Podolski, France forward Olivier Giroud and Spain midfielder Santi Cazorla.
Podolski, 27, maintains this shows Arsenal can be thinking about an attack on the championship and not just securing third or fourth place again.
"The Premier League has five or six teams who can play for the title - and we are one of them. We really want to win this trophy." Podolski said.
"I hope I can score a lot of goals and make some assists to help the club in the Premier League."
If the Gunners are not to slip back to being also-rans again next season, then they will have to tighten up a defence which leaked 49 Premier League goals last term - some 20 more than champions Manchester City.
Laurent Koscielny found himself playing alongside several different central partners last season after injuries again took their toll at the back.
The France defender, 26, recently penned a new long-term deal and intends to do all he can to make the Gunners rearguard a secure unit.
"Now I know the Premier League - I am more mature and more physical," Koscielny told Arsenal Player.
"You know I like to be tactical and technical in my position, but I have worked hard to be fitter and stronger.
"Now I want to continue my progression with this club.
"I know I played a good season last year, but I want to do more for Arsenal this year. I want to win a trophy."
Arsenal duo Alex Oxlade-Chamberlain (ankle) and Theo Walcott (thigh) both pulled out of England's game against Italy in Berne with injuries, which could see them doubtful for Saturday's Premier League opener against Sunderland at Emirates Stadium.