Emergency services were called just before 2.30pm on Sunday, to reports of a man and woman in the water.
It is understoof the pair, believed to both be in their late 20s, entered the water after falling off a paddleboard.
The woman was later rescued and treated for hypothermia.
It has also now been reported that the missing man is Simon Daniels, a personal trainer from Cheshire.
Emergency crews rushed to the area and cordoned off all adjoining roads and footpaths.
A massive search operation was launched with fire crews, paramedics and police all in attendance.
Yesterday evening (Monday) the man was still missing in the water.
The search and rescue mission continued and a scene remained in place overnight.
A post on the Oldham Police - GMP Facebook page last night read: "The scene remains in place at Dovestone Reservoir.
"Specially trained officers are continuing to support the family of the missing person.
"Emergency services personnel are working in very difficult conditions and are doing everything they can.
"The search will continue tomorrow in daylight hours."
Visitors are still being asked to stay away from the area, which is located on the edge of Oldham and the Peak District National Park, while searches are carried out.
