Florentino has declared Mou's appointment among "the best decisions I've ever made", but Ecodiario says he is concerned that the Special One could still leave Madrid in the summer.
Mourinho assured Inter Milan president Massimo Moratti he would stay long-term, only to leave two years into his contract - and left the Nerazzurri in disarray as a result.
Florentino doesn't want to be caught out and has a list of possible replacements for next season headed by former Liverpool boss Rafa Benitez, ex-Chelsea manager Carlo Ancelotti and Arsenal's Arsene Wenger.
Ancelotti and Wenger have both knocked back Real in the past, but circumstances now favour Florentino should he make a move.
In Benitez's case, he'd only reject a Premier League return for the Real job, particularly with Jorge Valdano now jettisoned.