Wray, 50, who has been nominated by US President Donald Trump to lead the Federal Bureau of Investigation (FBI) after he fired James Comey from this position in May, is a former high- ranking Justice Department official.
"I do not consider Director Mueller to be on a witch hunt," he told Senate Judiciary Committee during his confirmation hearing.
Mueller, a former FBI Director and predecessor of Comey, has been appointed as a special prosecutor by the Department of Justice to look into the allegations of the relationship if any between the Russians and the Trump campaign during the presidential elections last year.
The question was raised by Republican Senator from South Carolina Lindsay Graham during Wray's confirmation hearing.
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"In light of the Don Jr email, and other allegations, that this whole thing about Trump campaign and Russia's a witch hunt? Is that a fair description of what we're all dealing with in America?," Graham asked Wray, who replied in negative.
Wray did not specifically respond to the question if Trump can fire Muller.
During the confirmation hearing, several Democratic Senators expressed their outrage over the firing of Comey on May 9.
"Rather, we find that rank and file agents of the FBI did, and continue to, overwhelmingly support James Comey. In addition, Deputy Attorney General Rosenstein told members of Congress that when he wrote his memo, President Trump had already decided to remove Mr Comey as FBI Director," she said.
Senator Patrick Leahy said that they have now learned that a number of members of the Trump campaign were eager to work and talk with members of the Russian organisation, even though they're an adversary of ours, about the campaign.
"I talk about this not so much in history, although we need to know exactly what happened, because we got to make sure it doesn't happen again," he said.
"To the members of this committee, any threat or effort to interfere with our elections from any nation-state or any non-state actor is the kind of thing the FBI would want to know," Wray said.
The FBI Director nominee was critical of the Russians.
"I think Russia is a foreign nation that we have to deal with very warily," he said in response to a question.
He acknowledged that in some situation they are an adversary of the United States.