"I believe we have an interest in moving the peace process forward in a variety of ways," Netanyahu told reporters before his weekly Cabinet meeting, Haaretz reported.
Netanyahu, who plans to travel to Egypt Tuesday, said he asked to meet with Mubarak after the conclusion of talks last week in Israel with Egyptian intelligence chief Omar Suleiman.
"I intend to continue this important dialogue," Netanyahu said.
Meanwhile, Netanyahu cautioned that a plan to secure the release of kidnapped Israeli soldier Gilad Shalit was far from certain.
Netanyahu has serious concerns about a Palestinian prisoner swap for Shalit, who has been held in Gaza since his kidnapping by Hamas militants in 2006, Haaretz reported.
Notable deaths of 2014 [PHOTOS]