Ferdinand was cut above his left eye at the end of the Barclays Premier League match which pitted United against Manchester City at the Etihad Stadium on December 9. Police said that, although the player had not wished to pursue the matter, they were still seeking the person who threw the object.
A spokeswoman for Greater Manchester Police said: "He (Ferdinand) did not put in a formal complaint about the matter. He was asked if he wanted to but he didn't. We are still making inquiries and trying to identify this person from CCTV footage."
Following a heated derby at City's ground, which United won 3-2 with an injury-time goal from Robin van Persie, Ferdinand was also confronted on the pitch by Manchester City fan Matthew Stott.
The 21-year-old, had to be restrained by City goalkeeper Joe Hart as he ran at Ferdinand.
Stott has been banned from attending football matches for three years after admitting that he encroached on the field of play and used insulting words or behaviour.