Sir Bobby Robson was approached after he was sacked by Freddy Shepherd, but didn't feel the job was right for him and told them "thanks but no thanks".
Now former Newcastle striker Mark McGhee has done the same.
Majority shareholder Vladimir Romanov launched his search for a new manager back in January, after John Robertson, George Burley, Graham Rix and Valdas Ivanauskas had all parted company with Hearts during his rein.
Motherwell manager Mark McGhee was close to holding talks with Romanov this summer but a last-minute change of heart saw him opt to remain at Fir Park instead.
Hearts' search for a new manager remains ongoing amid unconfirmed reports that Stephen Frail has been placed on gardening leave.