Updated 11:36 a.m.

Senators have reached an agreement that would almost double the number of federal agents along the U.S.-Mexico border, require construction of 700 miles of border fencing and provide money for aerial drones, according to several Senate aides who said the deal should ensure significant Republican support for an immigration measure that is expected to be approved next week.

Sen. Bob Corker (R-Tenn.). (AP)

Sens. Bob Corker (R-Tenn.) and John Hoeven (R-N.D.) later Thursday are expected to announce details of the agreement that they worked on in recent days with members of the bipartisan "Gang of Eight" who wrote the immigration bill.

"We've made significant advances," Senate Majority Leader Harry M. Reid (D-Nev.) said Thursday morning as he opened the Senate, saying he is "willing to look at any reasonable amendment" and expected to hear more from Republicans later in the day.