The Polish international transferred from Legia Warsaw to the Gunners late last month for an undisclosed fee in a long-term deal.
However, Arsenal boss Arsene Wenger may opt to farm out the 22-year-old on loan as he is competing with Manuel Almunia for second place in the pecking order at the Emirates Stadium behind Jens Lehmann.
Fabianski, who is understudy to Celtic's Artur Boruc in the Polish national team, has made four appearances for his country, while he was voted best goalkeeper in the Polish league in each of the last two seasons.
Racing already have two keepers in their squad - Tono and Juan Calatayud - and a move for Fabianski seems to have come at an unorthodox time given that head coach Miguel Angel Portugal left El Sardinero earlier this week to become technical director at Real Madrid.
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