The 32-year-old Spanish defender has attracted interest from Barcelona, who are reportedly looking for a replacement for Lucas Digne.
However, Emery has no intention of letting his first-choice left-back go to Catalonia.
"First, I knew Nacho Monreal in Spain when he was playing in Osasuna and in Malaga. After six years here, I came and I know him as a new Nacho Monreal," he said on Thursday.
"After two weeks, after two months and now, I can say that I am very happy with him because he is 32 years old but I think physically, with his performances with us in matches, he is playing with a very good level.
"The rest of that, for me, is very important. I think we need to find a new contract with him to stay with the Arsenal team."
Monreal moved to Arsenal from Malaga in the summer of 2013 for an undisclosed fee believed to be around £8.5m.
His current contract is worth around £65,000 a week, and expires at the end of this season.