The security officials want the fence to prevent any possible penetration from jihadi infiltrators and protect the new Timna airport, which is due to be completed next year. It will replace Eilat Airport and also handle flights if they are diverted away from Ben Gurion Airport.
"Security officials recommended the construction of a security barrier to protect the new airport which will be built at Timna," some 20 kilometres (12 miles) north of the Red Sea resort city of Eilat, the local media quotes an army spokeswoman as saying.
It however remains unclear whether the next government would approve the suggested construction.
The country also has a border fence with the Gaza Strip and barriers along its frontiers with Syria and Lebanon.
The huge steel fence that runs along the Syrian frontier through the Golan Heights was built after the Syrian civil war broke out, for fear of a spillover of fighting and an influx of refugees.
Israel also has a vast separation wall that runs through the West Bank, which it began building during the second Palestinian intifada, or uprising, which lasted from 2000-2005. Israel claims that it protects civilians from possible suicide bombing attacks.