The striker tough approach and clear interest in Turkish culture has made him popular with fans.
"An important offer has been received from Beijing Guoan for Podolski," said Galatasaray's sporting director Levent Nazifoglu.
"We are considering this offer. Whether this transfer is realised is dependent on the player," he said quoted by the Anadolu news agency.
He did not give a transfer fee but 7 million euros ($7.3 million) has been named as a possible sum.
Chinese Super League club Beijing Guoan is the club of former Galatasaray Turkish international star Burak Yilmaz who joined in 2016 from the Istanbul club.
Podolski, who retired from international duty this year, joined Galatasaray in 2015.
His tough approach and clear interest in Turkish culture has made him popular with fans.
But he has also endured injury problems and the club has been through a fallow period, finishing only sixth in the Super Lig last year.