Saturday's FA Cup fourth-round tie between the Reds and Manchester United was the first game between the rivals since the eight-match ban imposed on Liverpool striker Luis Suarez after the FA found him guilty of racially abusing United captain Patrice Evra.
Following Liverpool's 2-1 win, it emerged that police were investigating the alleged racist gesture.
The image was distributed on social networking websites and a number of complaints were made to police.
Before the match the stadium announcer warned supporters that racist and homophobic behaviour would not be tolerated.
It is understood that home supporters found guilty of such offences inside the ground would be subject to life bans from the club.
Speaking after the game, match commander Chief Superintendent Jon Ward said: "I would like to thank the majority of fans for their behaviour and co-operation.
"We knew this would be a busy operation and most fans can be proud that they acted as ambassadors for their cities and their clubs.
"Despite the large numbers of supporters from both clubs and lively atmosphere, only 17 people were ejected from the ground and, at this time, two people arrested during the policing operation, all for low-level incidents.
"As a matter of course, Merseyside Police monitors Twitter, other social networks and match footage during high-profile events such as this match.
"We can confirm that specialist officers are reviewing match footage, as a result of a picture posted on Twitter. This matter is now under investigation by specialist hate crime detectives and we are working with Liverpool Football Club to identify the man in question.
"We take all forms of offensive behaviour seriously, and we will always thoroughly investigate such claims. We cannot allow this type of behaviour to affect the enjoyment of genuine fans.
"We will continue with our efforts to deal with the small number of individuals who commit offences at football matches, in particular, with the continued use of football-banning orders."
Officers have released a still image of a man who may be able to assist officers, in connection with the alleged racist gesture.
