A Royal Mail spokesman said discussions about the possible move are underway with the Communications Workers Union (CWU) and people in the Holbeck delivery office on New Princess Street and Leeds City Mail Processing Unit (MPU) at Wellington Bridge.
The spokesman said: "If the move goes ahead, it would enable us to improve facilities for our customers in the LS11 postcode area. There would be no impact on deliveries to our customers.
"The proposed new location, in Leeds City MPU, has sufficient space for our LS11 delivery operations. It would also enable us to improve facilities for our people and for our customers in the postcode areas.
"This is part of Royal Mail’s ongoing transformation of its business to increase the efficiency of its operation as well as providing delivery offices which are fit for purpose for our people and for our customers. It will also have car parking for customers and offer extended opening hours.
"As a commercial business, Royal Mail is responding to the huge growth in electronic communications and decline in letter volumes, while seeing a high volume of parcels and online shopping which need to be delivered to customers.
"If this relocation goes ahead, there would be no impact on deliveries to our customers. The postmen and women who work in the LS11 delivery office would continue to serve the local communities, delivering a high quality service to our customers.
"If the move goes ahead, detailed planning would take place to ensure a smooth transition for our operations, our people and the service we provide to our customers. We have a strong track record of managing change and we would work with our staff and our unions to give them the opportunity to discuss the implications in detail. There are not expected to be any job losses if the move goes ahead. "