The SNP leader admitted the word "national" could be "hugely problematic".
Kennedy Funeral To Be On Friday
The funeral of Charles Kennedy will take place on Friday, the ex-Liberal Democrat leader's family said.
Large numbers are expected to gather for mass at noon at St John's Church in Caol, near his Fort William home, to pay their last respects.
The service will be led by Father Roddy McAuley, who has described Mr Kennedy as "a much loved and respected parishioner''.
Both of Mr Kennedy's parents - who died in recent years, his father during the general election campaign - were laid to rest at the church.
There is also to be a memorial service at the University of Glasgow, where he served as rector, on June 18 and another in London at a later date.
Mr Kennedy died suddenly a week ago at the age of 55 after suffering a major haemorrhage as a result of a long battle with alcoholism.
In a statement, the family said: "This will be an opportunity for Charles' family and friends, the local community he loved and served for so long, as well as his political friends to bid him a fond farewell.
"The police have informed us to expect large numbers of people and we will make arrangements for the service to be piped outside should the church be full to overflowing.''
Mr Kennedy's body will be buried at Clunes, Achnacarry.
The family said: "We would like once again to thank the various authorities who have helped us through this difficult time.
"We have been touched by the care and sensitivity shown to us by the police, ambulance personnel, the office of the procurator fiscal, the registrar and Mike McFall, funeral director.
"We would also like to once again voice our heartfelt thanks to the public whose response has been so warm.''
A police watchdog probe was launched after the remains of the 52-year-old were found in a house in Dumfries in February last year.
The accident happened at about 7.50pm on Thursday in Moodiesburn, North Lanarkshire.
More than 70 firefighters were needed to bring the blaze under control at Blochairn Fruit Market in the early hours of Thursday.
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