"He has been saying to me for years: 'It will be you'," di Falco told the French newspaper "LaCroix" (Wednesday).
According to the report, the 82-year-old was contacted by Delon's family asking whether he would like to conduct the actor's funeral next Saturday.
According to the report, the actor had requested to be buried on his estate in Douchy near Paris before his death. The Catholic funeral is to take place in a private setting.
Di Falco is accused of having sexually abused pupils in the 1970s as headmaster of the public school Saint-Thomas-d'Aquin in Paris and was subsequently charged.
The court proceedings were initially discontinued in 2018 due to the statute of limitations for the alleged offences.
However, a court of cassation lifted the statute of limitations in 2022 and civil proceedings against di Falco are ongoing. The bishop himself has always denied the alleged offences.
Delon's partner already buried
di Falco held various positions within the French Catholic Church. Among other things, he was spokesman for the French Bishops' Conference from 1987 to 1996, founded the Catholic television channel "KTO" in 1999 and, according to "LaCroix", acted as a kind of counsellor for celebrities and artists in the 2000s.
In 2017, di Falco presided over the funeral of actress Mireille Darc, who was Alain Delon's partner for 15 years. This event had touched the actor and the two men had cultivated "bonds of friendship" ever since, di Falco told the newspaper.
Delon therefore also wanted a Catholic funeral and asked the bishop to preside over the ceremony.
The French film star Delon died last weekend at his home in Douchy near Paris.
The actor became internationally famous for his role as a ruthless killer in "The Icy Angel" (1967) and was honoured with the Palme d'Or for his life's work at the Cannes Film Festival in 2019.
In the same year, he suffered a stroke from which he never fully recovered.