Ferdinand was cut above his left eye during United's Premier League clash with Manchester City at the Etihad Stadium on 9 December.
Despite the former England defender's reluctance to pursue the matter, police continue to seek the person who threw the coin.
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 the derby clash, 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.
Stott, who had to be restrained by City goalkeeper Joe Hart as he ran at Ferdinand, was banned from attending football matches for three years on Friday after admitting that he encroached on the field of play and used insulting words or behaviour.