Di Matteo guided Chelsea to success in both the FA Cup and Champions League last season after taking over on an interim basis following the sacking of Andre Villas-Boas.
The cup victories led to the former MK Dons and West Brom manager being given the chance to manage Chelsea full-time, but Leboeuf, who was a team-mate of Di Matteo at Stamford Bridge, told Press Association Sport he believes the Italian needs to continue to win trophies if he is not to be sacked by Roman Abramovich.
When asked if Di Matteo needed to bring in more titles, Leboeuf said: "Yes, because he is the coach of Chelsea and they need to win trophies every year or at least fight for that.
"They are not the only challengers, there are seven clubs who could potentially win something and there are only four trophies overall.
"Chelsea won two of them last year in a special way but they have to show more because we expect something special from Chelsea and we want them to be the contender for the Premier League, and all of the cups, and we also want entertainment."
World Cup-winner Leboeuf, who was talking in his role as an ESPN football pundit ahead of the broadcaster's launch of its Premier League TV coverage, also refuted claims Chelsea were lucky to win their trophies last season but knows the Blues must hit the ground running at the start of this campaign.
He said: "It was really unexpected but it is nice to see players reacting to the new coach to save the season and save the club.
"We talked a lot about the luck they had, especially against Barcelona, but to win the Champions League you also need quality and I'm very thankful to have seen that and witnessed that.
"If you want to have a good season you don't want to start it in March, so hopefully they can start this weekend against Wigan because they have to make sure Chelsea is not the third or fourth placed team in the Premier League.
"They have the players and structure to do that, they just have to show it.
"They will finish in the top four, definitely. I want them to chase the two Manchester clubs, it will not be easy but every season is different and we will have to wait to make a statement, but they have certainly got the right players."
The club certainly have not stood still over the summer as they have added a number of players to their double-winning squad.
Marko Marin, Eden Hazard, Oscar and Thorgan Hazard have been signed and Leboeuf reckons the deeper squad is a necessity of the modern game.
"Don't forget they are not only playing in the Premier League but they are also involved in the Champions League, FA Cup and League Cup and when you are fighting for all those trophies you need a strong squad," he said.
"You need to make sure if you have injuries and suspensions you have a squad that is good enough and will fight.
"It is an understanding of how difficult and demanding modern football is and only 11 players can play. It will be hard for Di Matteo to keep 25 players happy.
"The only man I've ever seen achieve it is Jose Mourinho - and keeping all of his players will be the hardest thing for Di Matteo this season."