A number of postal workers in Skelmersdale in Lancashire have threatened to walk out if they are forced to deliver free copies of The Sun later this week.
The Sun, which has planned a nationwide drop of its free World Cup-themed promotion, has agreed not to send out copies in Liverpool, where there is still widespread anger over the way it reported the 1989 Hillsborough disaster.
However, the tabloid newspaper is still set to go out in some areas of Merseyside, because they do not have Merseyside postcodes.
The Royal Mail said any concerns would be handled "with fairness and dignity".
The Sun published a full page apology in 2004.
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The latest weather update plus viewers' photos for ITV Granada
Not a bad Bank Holiday weekend - mostly fine, sunny and warm! Always warmest further west
Mainly low to moderate over the next few days... small amounts of grass pollen in the air in the warmest, driest weather