The Edinburgh club made their move on Friday, following the end of the Clydesdale Bank Scottish Premier League season.
Hearts Want Ex-Toon Striker As Manager!
McGhee steered Motherwell to third place and UEFA Cup qualification in his first year at Fir Park, while Hearts finished in eighth.
Motherwell statement: "Motherwell Football Club can today confirm that it has received an official from Heart of Midlothian Football Club, seeking permission to speak with current manager Mark McGhee about the vacant managerial role at Tynecastle.
"After consideration, the Motherwell FC Board of Directors have decided to refuse this request."
*1977/91 M.E.McGhee 99/13 36
Two spells at Newcastle and they couldn't possibly have been so different. He came from Morton for £150,000 and looked as though he had the skill to make it, but always failed to deliver. He lacked strength and pace. But he went to Aberdeen and became a superstar. Capped by Scotland, he won Scottish Championships and Scottish Cups with both Aberdeen and Celtic. As well as European Cup Winners Cup medal with Aberdeen. Signed for Newcastle for £200,000 and hit it off with Micky Quinn straight away.