The general manager told Sky Sports that the Bundesliga outfit will not be pursuing Podolski this summer.
“Lukas Podolski is a great footballer, I like him,” Sky Sports quotes Eichin as saying.
“But we do not need to discuss such rumours. It is totally unrealistic for us to make a move for him.”
Podolski joined Inter on loan in January but struggled to settle in and the Italian giants will not make an offer to sign him on a permanent deal.
The Germany international is expected to leave Arsenal in the summer and Galatasaray have expressed a strong interest.
The Lions are reported to have held talks with the World Cup winner who only has one year remaining on his contract.
Galatasaray won the league and cup double this season. The Lions have won the Süper Lig a record 20 times and the cup 16 times. The Istanbul giants have booked a place in the Champions League group stages next season.