The Finn has held talks with the Iron over a move to Glanford Park as the Iron seek a replacement for Ian Baraclough.
Killie have gone from battling relegation last season to pushing for European qualification this term since Paatelainen took charge in the summer.
"Mixu has been given permission to speak to Scunthorpe but we are obviously keen to keep him," Killie chairman Michael Johnston told STV.
"We have no intention of letting him go easily. The disappointing thing is that success brings about this sort of situation. He has had a fantastic season with us."
Paatelainen has previously managed Cowdenbeath and HIbernian in Scotland, as well as Turun Palloseura in his native Finland.