The Blues are currently on their longest winless streak in the league for a decade, having failed to record a victory for five matches, and slumping from top spot to fourth in the table.
Missing his chance: Didier Drogba misses his last gasp penalty for Chelsea at Tottenham last weekend
Desailly and Leboeuf marshalled the Chelsea defence the last time the club went on such a poor run, during the middle of which manager Gianluca Vialli was sacked.
Leboeuf, who spent five years at Stamford Bridge until 2001, rejected suggestions an improved performance in Sunday's 1-1 draw at Tottenham heralded the 'turning point' in the champions' season.
He added: 'It is hard for me to criticise my former club but I said at the beginning of the season that I didn't think they would be winning the championship.
'I love them but I really feel they are at the end of the cycle.
'When I saw them flying at the top, I wondered if I knew anything about football any more but now we are seeing the truth and reality of that club and those players.
'They need to do something at the end of the season where they will need to sell and buy players.
'Of course, they didn't have a bad game against Spurs but one or two years ago that match would have been won by Chelsea.
'I really feel Chelsea is not Chelsea any more. I am sad about that. We need a new Chelsea for next season.'
Desailly, who spent six years at at the club and played alongside Leboeuf both in their 2000 FA Cup triumph and France's 1998 World Cup final win, added: 'When you look at the games at the beginning of the season, you thought, 'Wow, Chelsea are going to crush the Premier League from beginning to end'.
'It's been six weeks really where Chelsea have been awful.
Back in the day: Leboeuf playing for Chelsea in a FA Cup tie against Nottingham Forest in 2000
'I am annoyed they haven't been able to bring in a top-class player who can improve the energy of the team.
'It looks like Chelsea want to bring their young players into the team but they have not had enough experience to hold the team together.
'I am not sure if Chelsea will be able to win the title but they will be around the top.'
Vialli was axed after a four-match winless run - which eventually went to six games - but Desailly rubbished suggestions current boss Carlo Ancelotti might suffer the same fate.
'I laugh a little bit when I hear this because three months ago he was the man of the moment,' Desailly said.
It's not going according to plan: Chelsea boss Carlo Ancelotti
'He helped Chelsea win the league and the FA Cup and could do no wrong.
'Yes, he is having a difficult time at the moment and I'm sure he doesn't know himself what is going wrong.
'I'm sure he will build their confidence back up for them to perform well again.'
Chelsea are now three points behind new leaders Manchester United, having played a game more, ahead of Sunday's crunch clash between the sides.
Desailly believes the champions' season hinges on the outcome of the game.
'Yes, definitely,' said the 42-year-old, pointing out injuries tostar players had been costly and heralding the return of Frank Lampardas 'key'.
'It is a great chance for these players to prove themselves. Whentop-level players have to face other top sides, it is very good forthem as often there is that extra bit of desire.'
Leboeuf added on ESPN: 'The vertical column of John Terry, MichaelEssien, Lampard and Drogba are back and that's important but it will bea tough game against United.
'They have to win and then at least draw against Arsenal if they want to keep surviving in the competition.
'The positive thing I can say about Chelsea is that they haven't had any luck.'
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