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.
More top news
The Betfred Super League fixture between Wigan Warriors and Widnes Vikings scheduled for this Friday (February 24) has been postponed.
Around 800 properties in the North West remain without electricity, as engineers from Electricity North West work to restore power.
Wayne Rooney has announced he is staying at Manchester United in a statement released on Thursday.