The MLS club are said to be eager to pair the German striker with club captain Kaka ahead of the league's transfer window opening next month.
Podolski, 30, made just two starts and 11 substitute appearances for Arsenal over the first half of last season before joining Italian giants Inter Milan on loan for the rest of the campaign.
However, the German World Cup winner managed just one goal in 18 games during his time with the Serie A club, while Gazzetta dello Sport even named him the league’s second worst signing of the winter transfer window.
With another 12 months left on his Arsenal contract, the 124-times capped international is now set to return to the Emirates Stadium ahead of next term but, having fallen out of favour with manager Arsene Wenger, a permanent switch elsewhere is expected.
Speaking on his future earlier this week, Podolski told Sky Sports: "Things can always change, but if needs be I will remain at Arsenal next season. They are a great club and I think I can help them. I can confirm there has been no interest from [reported suitors] Werder Bremen.
"You can take experience from everywhere you play abroad, even if it was not my best year from a sporting perspective, but I still have many years ahead of me and a burning desire to play football."
With first-team opportunities set to be limited with the Gunners, though, one potential option for Podolski could be to follow the likes of Steven Gerrard and Frank Lampard across the Atlantic to MLS.
Expansion franchise Orlando have even been named as a possible destination, with general manager Paul McDonough and head coach Adrian Heath said to have made the Gunners misfit their top target ahead of the opening of the summer transfer window next month.
The Florida-based outfit sit in fourth-place in the Eastern Conference 14 matches into their inaugural campaign, having recorded four wins, five draws and five defeats, but have struggled to kill off games without an experienced goalscorer to link up with club captain and Brazilian superstar Kaka.
Rookie Cyle Larin has performed well of late, bagging five goals in eight starts, but, with the 20-year-old Canadian and fellow front men Bryan Rochez both expected to be at the Gold Cup next month, the club remain desperate for more firepower.
Manchester United’s Javier Hernandez has been mooted as another potential target in recent months, with Heath even admitting their interest in the Mexico international, but he believed to be keen to remain in Europe following a season-long loan at Real Madrid.
FutbolMLS.com note that Podolski would be willing to make the switch to Florida but, as usual, the biggest obstacle to a potential move remains finances.
The Polish-born forward is earning a reported £100,000-per-week at present and, while Arsenal could assume a portion of his wages, the MLS side would still have to find some way to free up a Designated Player slot with all three currently filled.
There could be other potential stateside suitors, of course, with the New York Red Bulls looking like a good fit for him on paper, but whether Orlando themselves have the means to make a deal happen remains to be seen.