Gutierrez's current deal expires at the end of the 2014-15 season and although the Argentinian only just returned to action last week, following 11 months on the sidelines due to his cancer treatment, he wants more.
The 31-year-old came off the bench in Newcastle's 1-0 loss to Manchester United on Wednesday, receiving rapturous applause from the St James' Park faithful as he came onto the pitch.
"I'm just living day by day. All I can do is work hard in training and work as hard as I can," Gutierrez said on Friday.
"I'm going to fight for my place - I always try to do that. I'm recovering.
"I'm healthy and I'm feeling strong - now I have to wait for my opportunity and fight for that.
"Now I have three months to do my best and we'll see what happens."
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