The French World Cup winner warned the Blues not to rest on their laurels after last season's Double triumph.
Desailly, 41, won the World and European Cups, and two Champions League trophies before joining Chelsea in 1998, playing 159 league games for the Blues.
"We thought we were untouchable, maybe even thinking it was easy. Yet they went out and signed George Weah, then the best player in the world. 'Pow!' It hit us. Here we thought we couldn't get better then he arrived and we were up and running again. He lifted us from our settees.
"The club needed it, I needed it. We felt strong once more, ready to go forward.
"The following year five Dutchmen arrived, top names but somehow it didn't work in the same way as Weah. So that is why Chelsea's next signing must be a significant one. A world-class player, no matter what the cost.
"You can't fight off age, so some need a boost. It must come in the way of a Weah."