Egypt has deployed at least 3,000 extra security forces near the border with the Gaza strip, according to officials.
The tunnels are located in an area known as the Philadelphi Corridor
The move comes a day after an Israeli newspaper reported that the Israeli government planned to attack the border region with precision-guided rockets.
Maariv reported Israeli troops would try to destroy tunnels allegedly used by Palestinian militants to smuggle arms from Egypt into the Gaza Strip.
Egypt says the possible Israeli mission could threaten 20,000 of its civilians.
The men from the police's central security force will join a 750 border guards already deployed in the area known as the Philadelphi Corridor.
An Egyptian official told Reuters news agency in Cairo that reinforcements were requested after the Israeli report and over "fears of Palestinian militants breaching the border wall between the Gaza Strip and Egypt".
The Israeli newspaper reported on Friday that precision-guided weapons would be used to penetrate underground and destroy the tunnel network that Israel says honeycombs the area, which is 11km (6.5 miles) long and about 100m (330ft) wide.
The decision to use "smart" bombs may be a substitute to reoccupying the region, the newspaper said.
Israel says it has been unable to control weapons smuggling into Gaza since it withdrew its forces from the Gaza Strip last year.
Israel says huge amounts of munitions have been smuggled into Gaza via the tunnels. However, little evidence has been presented to support the use of such weaponry by Palestinian militants in Gaza.