Stephen Dodd tweeted an image of solicitors Asif Bodi and Abubakar Bhula on prayer mats in a stairwell.
He captioned the tweet: "Muslims praying at half time at the match yesterday. Disgrace."
The Premier League club reported the tweet to Merseyside Police following a number of complaints.
A number of social media users shared the photograph, taken during Liverpool's FA Cup quarter-final against Blackburn on 8 March.
In a statement it said police had now referred the issue back to the club, which was "currently in the process of determining the appropriate action to take".
It added:  "Liverpool Football Club would like to remind its supporters that it does not tolerate any form of discrimination and is committed to ensuring that the club and Anfield provides a welcoming and safe environment for all fans regardless of race, religion, gender, age, disability or sexual orientation."
The club said a further statement would be made in due course.
Speaking last month, Mr Bodi, 46, from Preston, told the Liverpool Echo: "We have a small window in which to pray, a bit like the transfer window in football. Once that closes the chance has gone.
"That day, the time came for prayer and the window would have closed before the game finished so we did it at half-time.
"Most people are absolutely fine with it...but it only takes one or two people to react in the wrong way and you could have a nasty situation."
Liverpool FC is considering what action to take against a supporter who branded two Muslim fans "a disgrace" for praying during half-time at a match.