Reliable sources independent of each other identify the teacher as Jacqueline T. Fruge, an English teacher.
Principal Mitch Fontenot and School Supt. Joseph Cassimere declined to comment on the matter.
Fruge, a 1992 EHS graduate, had been on the faculty since 1997.
Police said a formal complaint has not been received, though they are looking into the matter.
Meanwhile, former Crowley High assistant football coach and Super Bowl XX participant for the Chicago Bears Keith Ortego has had his misdemeanor case involving a student put in the Acadia Parish Pre-Trial Diversion.
He was charged in June with prohibited sexual conduct via telecommunications between an educator and student.
His case was on the Nov. 22 trial docket but put in the diversion program.
Once he completes the program, the charge will be dismissed by the prosecutor.