Cathro was dismissed by the Tynecastle club this morning after the Jambos crashed out of the Betfred Cup group stages last weekend, ending an unsuccessful spell for the 31-year-old since arriving in Gorgie in December.
Former Hearts captain Pressley is the 4/1 favourite with Ladbrokes to be the next boss. Pressley is currently available after leaving Fleetwood Town in July last year. He has also managed Falkirk and Coventry City.
Paul Hartley, who departed Dundee late last season, is the 5/1 second-favourite.
St Johnstone manager Tommy Wright is 12/1, while ex-Hibs manager Alan Stubbs is priced at 20/1.
Odds to be next manager of Hearts: 4/1 Steven Pressley; 5/1 Paul Hartley; 10/1 Gary Naysmith; 10/1 Allan Johnston; 12/1 Jim McIntyre; 12/1 Tommy Wright; 16/1 David Weir; 20/1 Alan Stubbs; 20/1 Alex McLeish; 20/1 Terry Butcher; 20/1 Stephen Craigan; 20/1 Jim Duffy; 20/1 Kenny Shiels; 20/1 Barry Ferguson; 20/1 Ian Baraclough; 20/1 Jackie McNamara; 25/1 Gary Locke; 25/1 John Hughes; 25/1 Mixu Paatelainen; 25/1 Ronny Deila