Reports in France had suggested that the big-spending Ligue 1 runner-up was poised to make a move for Wenger, with current coach Claudio Ranieri set to be relieved of his duties at the end of the season.
Wenger's own future has been shrouded in doubt in recent weeks as he continues to stall on signing an extension to his Gunners deal, but he has distanced himself from talk of joining Monaco.
Speaking to the BBC after beating Norwich City 2-0 on Sunday he said: "I wish Monaco well, but there is no interest there."
The win at Norwich - sealed courtesy of goals from Aaron Ramsey and Carl Jenkinson - saw the return of Jack Wilshere from a foot injury, with the midfielder coming off the bench just after the hour mark.
Wenger was in no doubt over the 22-year-old's availability for the World Cup, with Roy Hodgson set to name his England squad on Monday afternoon.
"The World Cup is one month so it is plenty of time," he added. "He can play now so it just shows you that there is no problem with him being available for England."
The Frenchman added that fellow World Cup hopeful Alex Oxlade-Chamberlain is also close to full fitness following a groin injury, hinting that he could be ready to face Hull City in the FA Cup final next Saturday.
"He should be back into our squad on Wednesday for normal training. He will be available for Roy to pick him and I wouldn't be surprised if he’s picked."