We are never actually told specifically who suggested Charlie would be a suitable subject for the experiment that changes his life so drastically. However, there are hints that we can pick up that suggest that Dr. Strauss contacted the Beekman School for Retarded Adults and spoeke to Miss Kinnian to ask for a suitable candidate. Notice how in the third progress report, Dr. Strauss tells Charlie that Miss Kinnian had given them a report about him:
He said Miss Kinnian tolld him I was her bestist pupil in the Beekman School for retarded adults and I tryed the hardist becaus I reely wanted to lern I wantid it more even then pepul who are smarter even then me.
Thus we can infer that Dr. Strauss and his scientific team contacted the school and asked for a potential candidate that they could use for a suitable case study. Miss Kinnian, who is obviously impressed with Charlie and his dedication to his studies, suggested his name, which is how Charlie found himself the subject of this intelligence experiment.