The Germany international was pictured arriving in Milan wearing an Inter scarf on Friday, but no official announcement regarding a deal has yet been made.
However, Podolski appears on the verge of completing the move after saying his goodbyes to Arsenal via social media on Saturday.
"I can't express in words my gratitude towards Arsenal fans for all they have done for me in my years in London," he said via his Instagram account. "Please know my heart always holds a place for you.
"I've loved every minute playing for Arsenal and I hope I have left my mark on the club and fans alike.
"Hopefully we shall meet again."
Podolski has had a frustrating time with Arsenal, scoring 31 goals in 81 appearances for the London-based Premier League club but starting just 55 games.
Arsenal manager Arsene Wenger has not started Podolski in the Premier League this season, with the 29-year-old striker making just seven substitute appearances, prompting his impending move to Inter.
It is expected Podolski will join Inter on loan for the rest of the 2014-15 season.
