PARIS — As tensions in Ukraine mount anew, veteran diplomats are starting to think quietly about a way out of the worst East-West crisis since the end of the Cold War.

It may seem a poor time to imagine a revamped security architecture for Europe when a frail cease-fire in eastern Ukraine is violated daily. The United States and the European Union have imposed three waves of sanctions on Moscow over its annexation of Crimea and its support for pro-Russian separatists in southeastern Ukraine — to no avail.

Yet despite President Vladimir V. Putin’s diatribes against the West, neither Russia nor Europe has an interest in a long-term confrontation. The current conflict has already damaged both sides’ economies and could undermine stability across Eastern Europe.

As a result, wise diplomats like the former German ambassador Wolfgang Ischinger, chairman of the Munich Security Conference, and Igor Y. Yurgens, chairman of the Institute of Contemporary Development in Moscow, who is close to Russia’s prime minister, Dmitri A. Medvedev, are scouring the diplomatic handbook for a possible exit.