"The club made it absolutely clear from the outset we intended only to trademark our own copyrighted version of the Liver Bird in specific and relevant categories and not challenge the use of other variations," said club spokesman Ian Cotton.
"But we have listened to the views expressed by many people and recognise the concerns raised over such an iconic image, which has been associated with the city of Liverpool throughout its history.
"As such, we have decided to withdraw our application to trademark the Liverpool FC club crest rendition of the Liver Bird.
"The problem of counterfeit Liverpool merchandise remains and we look forward to discussing with the council how we can best work together with their support to tackle this significant issue."