The 24-year-old has established himself as a crucial player for the Ligue 1 side, making over 200 appearances over the past five years.
Fabinho was instrumental in helping Monaco win the French title last season but is now determined to pursue his career elsewhere.
"If the right move comes up, perhaps a change in league or to a club with a bigger structure and higher ambitions, I would love that," the Brazilian is quoted by Goal.com as saying.
"My time at Monaco has been great, I managed to win a title, now I believe my time here might be coming to an end.
"I know that the club's goal is to take second place [in Ligue 1] and earn a spot in the Champions League, not to sign big-name players but rather youngsters to give them their start.
"I believe that I have been through that, I came here as a nobody, made my name in the club, achieved things; so maybe I need something new, a new challenge."
Manchester United and Atletico Madrid have been linked with Fabinho in recent months.