The ex-England captain, 31, will stand trial at Westminster Magistrates' Court on 9 July accused of a racially-aggravated public order offence.
Mr Terry's barrister, George Carter-Stephenson QC, has now said he is considering making the application.
Bad character applications are used to cast doubt on a witness's evidence.
The trial relates to a comment allegedly made and caught on camera to the Queens Park Rangers defender when the two teams played last October.
According to the Crown Prosecution Service, "bad character" in criminal proceedings means "evidence of or a disposition towards misconduct".
Mr Carter-Stephenson said: "There is likely to be an application for bad character against Mr Ferdinand about two incidents."
No details were given about what these incidents were.