The FA Cup third round tie ended 5-1 in Liverpool's favour, but was overshadowed by the sight of a visibly upset Adeyemi exchanging words with a section of the Anfield crowd.
The club earlier released a statement saying: "Liverpool Football Club continue to work closely with Merseyside Police to establish all the facts surrounding the incident that occurred during last night's game.
"We take this matter extremely seriously and have today provided the police with the evidence we currently have available to us.
"This includes CCTV coverage and still photography of what we believe to be the relevant part of the stadium, statements from matchday stewards in that area and full access to all the footage captured by the cameras filming the match for our in-house TV operation.
"In addition, we have examined records of the tickets purchased in that part of the ground to see if they provide any additional information and have passed that on to the police. Finally, we would also urge any of our supporters who witnessed this incident or saw the individual involved and who have not already done so, to contact either the club or the police."
The man, from Aintree, is being questioned by officers from Merseyside Police who are investigating the incident which took place in the second half of the match at Anfield on Friday.
The news comes just hours after John Barnes insisted racism remains a huge problem in English football. However, the former England international did defend Liverpool's stance against issues of a racial nature, insisting the club are not "soft" on such matters.