The 28-year-old is becoming increasingly frustrated by the lack of first team opportunities at the Emirates and is set to leave in the winter.
With his contract due to expire at the end of the season, the Pole should be available for a nominal fee in January.
According to Daily Mirror, Schalke are prepared to offer Fabianski an escape route from the Emirates as they continue their search for a new number one.
The Miners have reportedly agreed to sign Fabian Giefer from Fortune Dusseldorf, but the talented keeper is set to arrive in the summer when his current contract expires.
Schalke officials are, therefore, hoping to sign Fabianski at the earliest opportunity and they expect him to slot straight into the starting line-up, with first choice keeper Timo Hildebrand far from impressive this season.