Boeing Co. has opened talks to sell airliners to Iran in what would be one of the highest-profile deals between a U.S. company and Tehran since the West lifted nuclear sanctions on the country in January.

Iran—eager to re-establish ties with Western companies after the deal to limit its nuclear program—quickly signed several landmark agreements with European companies to signal it had re-entered the international market. Agreements with U.S. companies have been slower to materialize, though, increasing the importance of a...