“I don’t want to give it away — it’s an asset,” Mr. Gehry said. “It’s the one thing in your life you build up, and you own it. And I’ve been spending a lot of rent to preserve it.”

Mr. Gehry, 78, is among a small but influential number of celebrity architects who are considering selling their archives — which can include tens of thousands of objects, from multiple large-scale models and reams of drawings to correspondence and other records — even as they continue to practice.