If the built-up equity in your current home will be applied to the down payment on the new home, naturally the former will need to be sold first.
Some home buyers decide to turn their current home into an investment property, renting it out. In that case, the current home will not need to be sold. However, your loan advisor will still need to evaluate your risk profile and credit history to determine whether making a loan on a new home is feasible while retaining title to the old home.
Buyers often have a short time frame to sell their current home when relocating to a new city because of a job transfer. If you are moving but taking a position with the same employer, check to see if they offer relocation assistance to help offset some of the costs.