New York City officials are weighing an ambitious plan aimed at remaking a large swath of the Midtown skyline by encouraging building owners to demolish aging structures and replace them with new office towers, according to people familiar with the matter.

The plan, still being hashed out internally, would likely involve a major rezoning of arteries such as Park and Madison avenues, the people said. The new regulations would allow owners to erect larger, modern towers in what officials hope would be an incentive to knock down...