The full-back has moved to quell the fears of the club's fans by announcing that he has no desire to leave despite the departures of a number of high-profile players
Los Boquerones finished fourth in La Liga last season, but have been forced to sell players such as Santi Cazorla, Salomon Rondon and Joris Mathijsen, while others, including the highly-rated midfielder Isco, are also rumoured to be on their way out.
Despite the exodus of talent from the club, Monreal has quashed the reports suggesting he is also on the move.
"I am very happy here, from the first moment I got here I have felt very loved. I have no intention of leaving," the 26-year-old told reporters after Malaga's 1-0 friendly victory over Everton on Sunday.
"Offers? We talk a lot. Every day there are names of different teams linked with me but we must not pay any attention to that. My head is in Malaga and it would be stupid of me to think otherwise. We are in the Champions League and that is what we should be concentrating on, that is what occupies us."
Malaga were drawn against Panathinaikos in the Champions League play-offs on Friday, and will play the first leg of that tie on August 21-22.
When asked about the club's involvement in the competition, Monreal said: "The team are on a good physical level and have been training well. We realise that it will not be easy. We must group together and play as a team. The key is unity."
The player's fine performances last season were recently rewarded with a call-up to the Spain senior squad, after Sergio Ramos was forced to withdraw through injury, and the former Osasuna player is delighted that he has been given a chance for the national team.
"I am very happy that I have been called up. I was upset that I was not part of the European Championship winning squad in the summer, but now I have an opportunity and will give it my best."
Monreal last featured for Spain against South Korea in May.