The 26-year-old has fallen out of favour with the Ukrainian side and has spent the last two years out on loan.
He spent last season with Bundesliga side VfL Bochum, making 25 appearances, and was in the Premier League with Fulham in the 2006/07 season where he played eight times.
West Ham goalkeeping coach Ludo Miklosko has identified Lastuvka as the perfect back-up for Robert Green after previous number two Richard Wright moved back to Ipswich Town.
Curbishley said: "Ludo is very keen (on Lastuvka) and it's his recommendation. That hopefully will be wrapped up today."




