The Sun reported that the Gunners have had a £25million bid rejected for the 22-year-old defender.
But Monreal insists he will stay and fight for his place at the Emirates.
Nacho Monreal insists he is happy to stay at Arsenal despite the club targeting Kieran Tierney
Monreal said: ‘I belong at Arsenal. I have a contract and my idea is to continue playing for them.
‘I am not worried about the size of the squad.
‘Petr Cech decided to retire and we’ve lost Aaron Ramsey, Stephan Lichtsteiner and Danny Welbeck.
‘But I know the club is looking 100 per cent for players and I am sure they will come.’
Monreal and team-mate Sokratis share an ice bath after a training session in Los Angeles
Arsenal have seen a second bid of £25m rejected for Tierney because it involves too many add-ons, according to reports.
The Gunners were hopeful that their improved bid would be accepted by Celtic, in what would have been a record Scottish transfer.
But according to The Sun, Arsenal’s offer has been turned down due to the structure of the proposed deal.
The Scottish giants are open to letting Tierney leave for the Premier League but they are holding out for £25m upfront.
Unai Emery’s side are expected to make a third offer for the Scotland international as they look to wrap up his signing as soon as possible before the new season.