The 24-year-old admits he has always desired a move to England and has harboured ambitions of joining the Gunners since he was a child
The Gunners are widely expected to bolster their attacking options in the summer, having relied heavily on Olivier Giroud for goals this season.
Goal understands that Arsenal representatives have already made contact with highly-rated Real Sociedad attacker Antoine Griezmann to open talks over a possible £25 million deal.
And Riviere has now revealed he would be open to a move to the Emirates Stadium if an opportunity presents itself.
"England is my dream since I was a kid," he told L'Equipe. "I was dreaming of Arsenal.
"You have to believe and never let go. I'm good at Monaco today, I have three years left on my contract. There will surely be reinforcements this summer. We wills ee what happens".
Riviere has made 27 appearances in Ligue 1 for Monaco this season, scoring 10 goals.