The 24-year-old has found himself third choice at the Bundesliga newcomers and Bielefeld have allowed Stoke to run the rule over the Frankfurt-born custodian.
The Potters currently have shot-stopper Steve Banks on loan from Premiership strugglers Bolton and are looking into various goalkeeping options.
Muller has played for Frankfurt, Bad Homburg and Hannover so far in his career and may have to take a step down to win some first team action.
