The 64-year-old confirmed on Friday that he would be happy to continue as Gunners' boss beyond the end of the season when his current contract comes to an end.
Wenger said: "Look, I have said many times already, I have given my word to this club and that I want to continue where I am. That means to stay."
The Frenchman joined Arsenal in 1996 and, during his 18 seasons at the club, has led the team to three Premier League titles - the last of these in 2004.
During his time in north London, Wenger has been linked with managerial jobs at many top European clubs, most recently Monaco.
According to the Daily Mail, Monaco are prepared to offer Wenger a £12.4m-a-year deal - after tax - to take over from current manager Claudio Ranieri.
Wenger is a former Monaco boss, having already spent seven years at the club before being sacked in 1994 - the year they reached the semi-finals of the European Cup.