The Germany international linked up with the Nerazzurri in January on a six-month loan deal after limited opportunities at the Emirates.
However, the move has not really worked out for Podolski, who is yet to score for Inter in 12 Serie A appearances, eight of those being starts.
Mancini is a big admirer of the 29-year-old and would like to keep him at the San Siro beyond this term, but accepts the World Cup winner wants to return to the Gunners at the end of his agreement with the Milan outfit.
“We have this bad habit in Italy of not knowing how to wait for things,” the Italian said at a press conference on Tuesday.
“Not everything can happen quickly, particularly when you are moving from one country to another or from one club to another.
“That also applies to Podolski, who I rate as a great player and a great professional. His situation is a bit different because he’s on loan and he wants to go back to Arsenal, and that is how it will be.”