Get French Football News understands that the initial discussions between both parties have been positive and negotiations are soon to be getting into an advanced stage.
It is very possible as well that the current Benfica manager Jorge Jesus could become the next coach of Monaco and would be the heir to Claudio Ranieri despite having secured their path into the Champions League next season.
If Jesus was to be the next manager, the chances of signing Garay would rise substantially with it becoming almost a certainty for the 27 year-old to join the cashed up side.
With the League already rapped up, Garay has the chance to help his side further to gain more silverwate in the Europa League where they meet Sevilla in the final next week.