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.
Barcelona and big-spending Monaco have both been credited with an interest in Kompany as they look to bolster their defensive options.
However, Kompany has moved to play down the rumours and insists he is staying at City as he has "unfinished business" at the Etihad Stadium.
"Speculations and questions about next season.. I'm not going anywhere," Kompany said on Twitter.
"I love playing for City and I've still got some unfinished business."