Monreal has just one year left on his current deal and is thought to be in talks about extending his stay.
The Spaniard has been linked with a move to Barcelona and Arsenal will want to avoid a similar situation to Alexis Sanchez last year when they were forced to let him join Manchester United after failing to agree terms.
Despite talk of a potential exit, Monreal has embraced the new regime and has played in three of Arsenal’s first four Premier League games.
The defender has been with Arsenal since joining from Malaga in 2013 and Emery has now urged both parties to reach an agreement on a new deal.
“First, I knew Nacho Monreal in Spain when he was playing in Osasuna and in Malaga,” he said ahead of Arsenal’s trip to Newcastle on Saturday.
“After six years here, I came and I know him as a new Nacho Monreal.
“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.”
The defender is well placed to make a comparison between Emery and the legendary Gunners boss he replaced, Arsene Wenger.
And he’s revealed the difference in approach between the duo, particularly at Arsenal’s London Colney training ground.
“In training, he likes that every single player gives his 100 per cent in any moment,” Monreal said.
“Training is one hour and a half, [maybe] one hour 40, whatever, [and] all the time we must give our best performance.
“If we have to run, we have to do it, don’t save any energy.
“After that, he loves that we enjoy and have a good atmosphere in the group.
“While we are training, it is: ‘Come on guys, do everything’ and after you will have time to relax and enjoy with your team-mates.
“It is good for the team.
“That [the pitchside gym] is what they did on the first day.
“I wasn’t here but I saw it.
“At the moment, we haven’t used it too much so that’s a good point for us!
“But both managers [Emery and Wenger] like to have the ball, have long possessions and protect the ball during the games.
“Probably with Unai Emery, we work more tactically.
“He is a Spanish coach and in Spain we work a lot on tactics, set-pieces – I think we are improving in this aspect.
“This is our idea for this year – have more possession, don’t lose stupid balls in the middle of the pitch and be more compact than how we were before.”