Authorities in the South were ready to discuss the relief supplies needed, the scale of aid and how to transfer it and looked forward to a swift response from Pyongyang, the Red Cross said.
The statement was issued by the South's Unification Ministry, which handles inter-Korean affairs. The Red Cross has taken the lead in carrying out projects between the rival Koreas in the past, including reunions of separated families and supply of aid.
Heavy rains have hit the North's northwestern areas in recent days, flooding more than 4,000 homes in the regions of Sinuiju and Uiju, North Korean state media have reported.
North Korean leader Kim Jong Un personally inspected the flooded areas and expressed grave concern over the damage, state media said on Monday.
The region has been affected by heavy rainfall from Tropical Storm Gaemi in recent days, which caused a landslide killing 12 people in southern China and flash floods elsewhere.
There is a possibility of "significant human casualties" in North Korea, a Unification Ministry official said on Thursday. South Korea's TV Chosun reported more than 1,100 people and as many as 1,500 people are dead or missing, citing an unnamed government official.
On Thursday, the North's state media said there was work underway in the capital to prevent the flooding of the Taedong River that flows through Pyongyang.
The offer of help comes as relations between the two Koreas, which remain technically at war, have been particularly strained amid a hardline stance towards the North by Yoon's government.
Since late May, the two sides have been locked in tensions over North Korea's launch of balloons carrying trash to the South and Seoul response with propaganda broadcasts at the border, which angered the North.
It was not clear if Pyongyang would respond at all to the offer or agree to hold discussions. North Korea has cut off all lines of official communication with the South.
Clear assessment of damage and casualties from disasters in the North is difficult, as there are no outside humanitarian monitors present in the reclusive state.
More rain was forecast for Sinuiju on Thursday and early Friday, according to South Korea's weather agency.