The plan centred on a document delivered to opposition leader Isaac Herzog in September, but Netanyahu later pulled back and talks collapsed in October, Israeli newspaper Haaretz reported.
Spokesmen for Netanyahu and Herzog, who heads the Zionist Union coalition dominated by his Labour party, did not immediately respond to requests for comment.
The effort came as moves were underway to restart peace talks with the Palestinians through a process that would include Arab countries in the region.
Forming a unity government with the centre-left could have reassured Arab nations of his sincerity.
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The document reportedly delivered to Herzog in September was a proposal for a joint declaration reiterating their commitment to a two-state solution and their desire to seek a resolution with the Palestinians.
It came some seven months after a previously reported secret meeting between Netanyahu, Egyptian President Abdel Fattah al-Sisi, Jordan's King Abdullah II and then US secretary of state John Kerry.
Arab countries have previously offered normalised relations with Israel in exchange for resolving the decades-old Israeli-Palestinian conflict.
Under Netanyahu's plan, the draft document negotiated with Herzog was to be submitted at a summit in Egypt in October to launch a regional peace initiative.
The two men were then to announce negotiations for the formation of a unity government after returning from the summit, which ultimately did not occur, Haaretz said.
According to the paper, Netanyahu later told Herzog he wanted to resolve controversy surrounding the evacuation of a Jewish outpost in the occupied West Bank first, and talks later collapsed.