Apple's offer, disclosed in a filing to the U.S. District Court for the Western District of Wisconsin in Madison, comes five days before a trial is due to begin that centers on the issue of patent licensing.

During the trial, the two companies are expected to argue over licensing rates.

The patents in question are considered vital to the UMTS, GPRS, GSM and 802.11 standards in which they are used, so Motorola Mobility is required to license them to competitors on "fair, reasonable, and non-discriminatory terms," often referred to by the acronym FRAND.

Motorola Mobility is arguing for a royalty payment of 2.25 percent on each device.

"Apple would be willing to pay a Court-ordered FRAND rate of less than or equal to $1 per covered product on the going-forward basis," it said in the filing. "This is the rate that Apple believes is appropriate in these circumstances for Motorola's portfolio of cellular and WiFi essential patents."