An online opinion poll in Catalan sports daily El Mundo Deportivo, in which 25,860 votes had been registered by Wednesday morning, gives 42 per cent of the votes to former Chelsea boss Mourinho, 30 per cent to Arsenal's Arsene Wenger and seven per cent to Espanyol coach Ernesto Valverde.
Five per cent of the votes go to former Real Madrid boss Fabio Capello and to Holland manager Marco Van Basten, three per cent to Valencia coach Ronald Koeman and to former Italy boss Marcello Lippi.
A similar poll taken by Madrid sports daily Marca gives the same 42 per cent to Mourinho, with 19 per cent for former Spain manager Javier Clemente, 18 per cent for Van Basten, 11 per cent for Capello and nine per cent for Valverde.
Rijkaard is under massive pressure as Barca are third in La Liga, four points behind historic rivals Real Madrid.
The Dutchman is also perceived by most fans as being insufficiently hard and demanding with stars like Ronaldinho and Thierry Henry.
A 3-0 win in the King's Cup away to third division Alcoyano on Tuesday will relieve some of the pressure on Rijkaard - at least for a few days.