In a poll conducted in Israel in 2011, an astounding 81% of Israelis supported EU membership. This is a big increase to a previous poll conducted in 2009 which showed 69% of Israelis supporting EU membership.
The European Union took a determined stance on Palestine: recognition of Palestine, labeling of products from the West Bank, humanitarian aid to Gaza, and etc. All these developments have placed the EU in a positive light among Palestinians.
In terms of a two-state solution to the current issue, support among Palestinians is 38% and in Israel its 50% in the summer of 2014 following the war in Gaza. The “two-state solution” will facilitate the creation of independent Israel and Palestine, and is one of the most popular approaches to resolving the conflict.
As the definition of "Europe" is fluid even within the European Union, Israel can technically be considered as being "European" [take Cyprus for example, which is closer to the Middle East than to Europe] and thus be a candidate for membership.
Every new candidate must adhere to the Chapters of the acquis which can be modified in Israel's case to include a two-state solution being approved and implemented. As both Israelis and Palestinians support this solution, the European Union can use the membership carrot to bring about the two-state solution.
For Israel the two-state solution and EU membership would not only secure its borders but also contribute to the peace it currently lacks. For Palestinians the implementation of the mentioned plan can lead to the realization of their own independent nation and a "trusted ally [i.e., the European Union]" could bring peace in the region.
The European Union needs to look beyond its current solution methods to not only secure the troubled borders it has with the Middle East and North Africa, but also bring peace in the region. The current methods have failed, and it is time to look at alternative ways of resolving these issues.