Taking into account the behaviour of some Cardiff city fans during and after thier clash with Leeds in the third round, local Council officials are worried that the police may not be able to cover both games.
Wirral Council leader Steve Foulkes said: "As Everton have been drawn at home on the same day, I will be writing to the Chief Constable of Merseyside Police, to ask if he has enough resources to adequately cover both games on the same day, or whether he should recommend to the FA that the fixtures be split to alleviate pressure on the police."
A Merseyside Police spokesman confirmed that talks were held on Wednesday over security arrangements for the Tranmere game, by adding: "The meeting discussed what the options were for the policing of the game. Our officers will also be liaising with the club to discuss all the issues as well as taking everything the FA says into consideration."
The game is currently sceduled for the 26th of January.