"Gutierrez has been the one who has stood out for me so far this season," Barnes told Newcastle's official website.
"We know he will have technical ability because he is from Argentina but his work-rate has been outstanding.
"It is that work ethic and willingness to work for the team which has impressed me most.
"And from what I hear his attitude will be like that all of the time.
"He has definitely caught the eye and should be a top player for Newcastle this season."