The Ligue 1 giants recently lost star striker Radamel Falcao for the remainder of the season through a knee injury, and are now rather short on firepower as they set about reeling in league leaders PSG.
With only three points between the pair at the summit of the French top division, the newly promoted Mediterranean outfit believe that they can overhaul their major rivals if a big name player arrives.
Hernandez has emerged as a genuine target over the course of the past week, with the Mexican ace said to have grown frustrated with life at Old Trafford.
Chicharito has been used sparingly by David Moyes this term, with only a handful of appearances, mainly from the bench, having been granted to him.
Monaco are ready to offer him an escape route, with the guarantee of regular playing time ahead of the World Cup.
Osvaldo is also on their radar amid rumours that he is free to leave Southampton just a matter of months after signing for them.
The Italian forward was involved in a training ground bust-up with Jose Fonte last week, and is believed to be seen as a toxic presence at the club.