Apple (Nasdaq: GOOG) and Google’s (Nasdaq: GOOG) Motorola Mobility unit are talking about a way to resolve part of their dispute over patents related to critical smartphone technology, according to a court filing.

The companies have been exchanging proposals on using binding arbitration to reach a licensing agreement over patents that are essential to comply with industry standards on how phones operate. Such an agreement could lead to a global settlement of all of their patent disputes, Apple said in a Nov. 15 filing.

Motorola Mobility first raised the issue of arbitration on Nov. 5, before a federal judge in Madison, Wisconsin, threw out a breach-of-contract case that Apple had filed. The Cupertino, California-based maker of the iPhone claimed its mobile-phone competitor was misusing standard-essential patents to demand unreasonable royalties.

“We have long sought a path to resolving patent issues and we welcome the chance to build on the constructive dialogue between our companies,” Google General Counsel Kent Walker said in a Nov. 13 letter to Apple that was filed with the court.

Apple, the world’s most valuable company, has argued that competing handsets running on Google’s Android operating system copy the look and unique features of its iPhones. A continuing battle with Samsung Electronics Co., which has the biggest share of the global market for smartphones, is being waged across the globe.

Even so, Apple has recently shown a willingness to settle some of the disputes. It announced a 10-year licensing agreement with Taiwan’s HTC Corp. on Nov. 10. The company earlier settled a patent dispute with Nokia Oyj.

“Apple’s goal has always been to find a mutual and transparent process to resolve this dispute on terms that are fair, reasonable and non-discriminatory without the threat or taint of exclusionary remedies,” Apple General Counsel Bruce Sewell said in a Nov. 8 letter to Google that was included in the filing.

Spokeswomen Kristin Huguet of Apple and Niki Fenwick of Google declined to comment.

Microsoft Corp. has its own battles with Motorola Mobility over standard-essential patents, and a non-jury trial is under way in Seattle. U.S. District Judge James Robart could issue a ruling establishing a fair rate for the Motorola Mobility patents. That could lead to an agreement between those two companies, said Victor Siber, former chief intellectual property counsel for International Business Machines Corp., and now with Baker Hostetler in New York.