The former U-21 Slovakian keeper made over 50 apperances for the Robins for who he signed back in 2007 from Czech side FC Brno.
The Czech born keeper has also had a trial at Everton back in 2007 and recently had a trial at Bristol City after his release from Swindon Town.
Brezovan turned out for Crewe in the 3-2 defeat to Aston Villa reserves on Tuesday.