The Finn has been interviewed by the Championship club as they step up their search to find a replacement for Ian Baraclough, who was sacked last week.
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Michael Johnston, the Kilmarnock chairman, gave Paatelainen permission to speak to the Yorkshire side but is still confident his manager will elect not to move to Glanford Park and has offered him a new contract.
Paatelainen met Steve Wharton, the Scunthorpe chairman, earlier in the week and is thought to be interested in making the switch.
Scunthorpe, second bottom of the Championship and five points from safety, are keen to have a new manager in place in time for their match against Norwich City next weekend, and have a shortlist of four.
Danny Wilson, the former Swindon manager, Phil Parkinson, once of Charlton Athletic, and Alan Knill, a one-time Scunthorpe captain now manager at Bury, are thought to be the others in contention.
Paatelainen has 15 months left on his contract, which is believed to include a buy-out clause that allows him to move to other clubs if appropriate compensation is paid.
Johnston said. “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.
“This has come out of the blue, I guess. But then again, it is no surprise Mixu is on the radar of other clubs . . . But we don’t want to drive this underground. It is better for all parties to be open and transparent.”