Gunners scouts had the 20-year-old watched in the tournament along with a few other players, and they returned with glowing reports for Arsene Wenger.
Cech plays for Sparta Prague in his homeland and is valued in the £3 million bracket by his club.
Arsenal have David Seaman, Stuart Taylor and Richard Wright on the goalkeeping books at Highbury and if Cech is snapped up by the club it could spell the end of the latter who has failed to shine since his £4.5 million move from Ipswich Town.
Wright could be allowed to leave for a cut-price £3 million with a number of Premiership clubs likely to be interested in his signature.