"A lot of people have said 'when do you think you'll be done?' Maybe the end of the year," King, who is a member of the Senate Intelligence Committee, told NBC broadcaster.
The senator noted that it was a very complex matter, which involved thousands of pages of intelligence documents, many witnesses, hence a lot of information needed to be processed.
"We are 20 percent into it," King said answering the question on how far the investigation has progressed.
On Wednesday, media reports emerged claiming that US Special Counsel Robert Mueller, who was overseeing a probe into Russia's alleged interference, was widening the investigation.
Russian officials have repeatedly denied any Moscow's interference in the US presidential election, saying such allegations are aimed at distracting public attention from instances of actual election fraud and corruption as well as other pressing domestic issues.