FIFA have rejected the transfer of Kevin Grosskreutz due to the paperwork being submitted without signatures according to LigTV.
The Germany international had agreed a three-year deal with the Istanbul Giants.
Galatasaray cannot however, register Grosskreutz until the opening of the next transfer window. The experienced winger will train with the Lions until January.
The 27-year-old winger has spent the past six years in Dortmund, making a total of 176 appearances for the Bundesliga giants.
Arsenal were also linked with a £3.7 million move for the Dortmund winger earlier in the year according to the Daily Star.
The versatile 27-year-old can play on either wing or at right-back. Grosskreutz provided four assists in 25 appearances for Dortmund last season.
Galatasaray are currently third in the Turkish Super League with six points after two games.
The Istanbul giants won the league title for a record 20th time last season earning the right to wear a fourth star on their crest.