Clubs in the Halifax League voted 28-3 against Queen's Road Muslims taking the vacancy in the new third division because they said the club did not meet the criteria.
Safdar Hussain, chairman of Queens Road Muslims, said: "We are having a meeting with the racial equality officer at Calderdale Council in order to contact the England Cricket Board. We have already been in touch with the Yorkshire Cricket Board and we are waiting to see if they can help us.
"Both these boards fund the Halifax League and their clubs, so if they are found to be not taking into consideration equal opportunities and racial harmony then they should decide if they should be funding them."
Mr Hussain said if the attempt failed, they would have no choice but to enter the Bradford Sunday League.
He said: "They gave us no real reason for refusing entry. It doesn't add up. Personally, it has not sunk in yet. We can't believe it happened.
"They did mention that the ground was not fit, but we spent thousands on the ground and even had an advisor for Yorkshire pitches inspect it and he gave a positive response. It is beyond us."
One cricketer, who plays in the Halifax League, said similar teams played a decent standard of cricket, but that wasn't enough.
"I have played with and against Asians at cricket and they bring nothing to the club such as practice and socialising - they turn up late, go and sit in their cars and leave after the game has finished."
A former Halifax player said Queens Road Muslims should not be allowed in the Halifax League because they don't have a clubhouse, serve food or alcohol.
Halifax League secretary Leyland Smith said a number of reasons had been given to the Queens Road Muslims, including the fact they had doubts about their field, their wickets, administration and they only had an eight-year tenure of the ground, when other grounds were asked to have 20 years.
He said: "They were refused on genuine grounds. Other clubs have been turned down a few times. Southowram is just one example, but they have gone away and put things right and eventually been given permission to join the league."