Chelsea boss Jose Mourinho values Belgium playmaker Eden Hazard at £200m after reported interest from Real Madrid.
Alan Pardew is weighing up chasing a big-name summer signing to boost Crystal Palace's profile.
The French-born Guadeloupean international scored 14 goals last season, including four in the 10-2 win over Greenock Morton as Accies mounted a late charge to secure promotion back to the Premiership via the play-offs.
The 31-year-old is in his second spell at New Douglas Park having returned at the start of last season after two years in Cyprus and Kazakhstan.
"Mickael did well for us last season and I'm delighted he has agreed terms to stay with us in the Premiership," Accies manager Alex Neil said.