Chelsea said they "categorically refute" the findings of FIFA's Disciplinary Committee and would appeal.
"Who would you want to sign in the summer," Chelsea asked their Twitter followers, providing a link to a 'Media Watch' section on their website which said the club was looking at AC Milan centre back Alessio Romagnoli as a potential target.
The tweet, which has been removed, outraged many fans, with one asking the club to sign a new social media team instead.
Others jokingly suggested Spanish keeper Kepa Arrizabalaga would have the final say following his refusal to be substituted by Chelsea coach Maurizio Sarri during extra time in Sunday's League Cup final defeat by Manchester City.
Chelsea were not immediately available to comment.
If Chelsea contest the ban they could operate in the close season transfer window while an appeal is heard by FIFA.
(Reporting by Rohith Nair in Bengaluru; editing by Ken Ferris)
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