The Real Madrid midfielder is set to be offloaded by the Spanish giants in the summer window, with Goal revealing on July 17 that Chelsea have edged ahead of the Gunners in the race to sign him.
And while Podolski, who shared an apartment with Khedira at the World Cup, insists he did not try to convince the 27-year-old to make the switch to Arsene Wenger's side during the duo's time in Brazil, he is keen to see him move to north London.
"I didn't have to [try to convince Khedira to join Arsenal]," he told Sport Bild.
"Sami knows how much fun he could have with me, Mesut [Ozil] and Per [Mertesacker] at Arsenal. We had a great time together at the World Cup and I would like it very much if he comes to London."
Goal understands that Khedira's £200k-a-week wage demands have put off the Gunners, clearing a path for Jose Mourinho's Chelsea to seal a deal, with Juventus having placed a £60 million valuation on the Blues' top target Paul Pogba.
Khedira played five of Germany's World Cup matches in Brazil but missed the final against Argentina through injury.