The Belgium international, who is the brother of Chelsea attacker Eden Hazard, scored 11 times and registered nine assists in 37 appearances for Gladbach during the 2017-18 campaign.
Sevilla have been credited with an interest in recent days, but Hazard has said that he 'feels good' at his current team.
"Sevilla are a great club," Hazard told RTBF. "They are a good team who play at the top of one of Europe's strongest leagues and compete highly in Europe almost every year, but Monchengladbach are strong too.
"Right now, I do not want to discuss my future as I still have things to do this season, then we can start to think about the next one.
"At the moment, I have a two-year deal with my club and whilst it is a shame we could not qualify for Europe, I feel good at this club and in this league."
Hazard joined Gladbach from Chelsea on a permanent deal in 2015.