Amartey, 21, was linked with Liverpool in December after his agent revealed Premier League scouts had been tracking him.
But the Ghana defender could now be heading to the King Power Stadium.
A Copenhagen press release said: "There has been rumours in the press about FC Copenhagen considering selling Daniel Amartey to the English club Leicester City.
"FC Copenhagen can confirm that we have received an offer on Daniel Amartey from Leicester City.
"Right now there’s talks between the two clubs.
"We'll send out new press release if agreement is reached."
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