The 32-year-old midfielder has said he may be ready to leave the Dutch side if they fail to make the knock-out stages of the Champions League, with the Premiership his preferred destination.
City have been scouting in both Germany and Holland and Stuart Pearce has been alerted to the potential availability of Galasek, who is a regular in the Czech national team.
Galasek is expected to be available for around £2m.