A complaint was made on March 14, a day after Chelsea's 1-0 quarter-final success in a fiery contest at Stamford Bridge, and was focused on the chant of "Chelsea rent boys" directed from the visiting supporters.
The Metropolitan Police said in a statement: "Officers at Hammersmith and Fulham borough received an allegation on Tuesday, March 14 of homophobic chanting at the Chelsea v Manchester United football match at Stamford Bridge on Monday, March 13.
"Following initial police enquiries it was concluded that the matter did not meet the threshold for further investigation and the matter is now closed."
The Football Association is aware of the chant, which has often been used in fixtures between the two clubs.
An FA spokesman said: "We have received a complaint about offensive chanting at this fixture.
"We take all complaints seriously and look to work collaboratively with clubs, players, managers, officials and safety officers towards eradicating all discriminatory and offensive chanting."
Manchester United and Chelsea next play at Old Trafford in the Premier League on Easter Sunday (April 16).
A statement from United read: "We are aware of a complaint to the FA.
"The club aims to work closely with Chelsea to identify anyone believed to have engaged in discriminatory behaviour at the game and will follow the terms of our official sanctions policy if necessary.
"In addition, we will liaise with Chelsea to determine any activity to discourage such behaviour before the next fixture."