Egyptian security officials have said they are digging steel tubes into the ground on their side of the border and are paving a road that will have devices along its route to monitor smuggling.
The US Army Corps of Engineers, which is reportedly involved, has worked with the Egyptians on preventing smuggling along this border for at least two years.
Palestinian smugglers in Gaza have built dozens, perhaps hundreds, of underground tunnels through the sand to bring a wide range of goods into the small territory, from food to fuel to cattle, to skirt Israel's economic blockade.
Armed groups, notably Hamas, also operate more secret tunnels to bring in weapons and these are often targeted by Israeli jets. After Israel's three-week war in Gaza last January the US said it would provide technical and intelligence assistance to Egypt to stop weapons smuggling into the strip.
Egypt's new wall will be about six miles long and "impossible to cut or melt", the Israeli newspaper Ha'aretz said. It said construction had already begun and that large slates of steel would eventually be buried into the ground. Joint Egyptian-American patrols had been seen on the Egyptian side of the border, it said.
Other reports said it would take 18 months to build. But Egyptian officials have not spoken publicly about the plan, saying they can do enough to halt smuggling without a wall.
Since Israel withdrew its soldiers and settlers from Gaza in 2005, Egypt has been allowed to deploy 750 lightly armed border guards in the northern Sinai to patrol the Gaza border.
But since Hamas won Palestinian elections in early 2006 Israel has tightened an economic blockade on the strip that has now spawned a vast smuggling industry.
The tunnels are dug deep and reinforced by wooden batons. Their entrances, under large tents, can be seen dotted along the Gazan side of the border. Hamas, which controls Gaza, effectively licenses the tunnels, providing electricity, taking a tax on smuggled goods and banning the import of drugs, alcohol and cigarettes.
Egypt is reluctant to take on full responsibility for Gaza's future and is under US and Israeli pressure to halt weapons smuggling.
Shortly after Barack Obama was inaugurated in January, just after the Gaza war, he promised help to Egypt to stop smuggling.
In early 2008 the US gave $23m in military aid to the Egyptians to stop the tunnels, sending in a team from the engineer corps to advise and train in several techniques, including ground-penetrating radar. Another plan was to build a deep canal along the border to prevent tunnelling.