The SNP leader admitted the word "national" could be "hugely problematic".
Kennedy Memorial Fund Set Up
A memorial fund is being set up by the University of Glasgow to commemorate the life of former student and rector Charles Kennedy.
The aim of the fund is to name a teaching area or lecture theatre within a new building being planned at the university.
The former Liberal Democrat leader studied politics and philosophy at the university, and sharpened his renowned debating skills during his stay in the city.
He was later elected rector of the university in 2008 and held the position for six years.
Hundreds of people attended Mr Kennedy's funeral in Caol, Fort William, in the Highlands last week. The father-of-one died suddenly at his home on June 1 at the age of 55.
A memorial service is to be held at Glasgow University this week, with family, friends and politicians expected to attend.
People will be given the opportunity to contribute to the fund at the service in Bute Hall.
Principal and vice chancellor Professor Anton Muscatelli said: "We feel that this would be a fitting and permanent tribute to Charles' life and work at the heart of a student-centred building."
The service will be led by the university chaplain, Rev Stuart MacQuarrie, and start with an academic procession led by a piper.
Prof Muscatelli, Mr Kennedy's lifelong friend Brian McBride and the presidents of the Glasgow University Union and the Students Representative Council will pay tribute to the former Lib Dem leader during the service.
Political figures including Gordon Brown, John Swinney, Sir Menzies Campbell and former spin doctor Alistair Campbell were among the mourners at Mr Kennedy's funeral last week.
Afterwards, Sir Menzies, who succeeded Mr Kennedy as Liberal Democrat leader, said: "It's often said about people, especially when they pass over, that they were the kind of person who would speak to everyone. But in Charles Kennedy's case, that was undoubtedly true."
Following the service, which lasted more than an hour, a lone piper accompanied the hearse and coffin from the St John the Evangelist church, which sits in the shadow of Ben Nevis.
Hundreds of people gathered outside as the funeral cortege began its final journey for the private burial at Clunes, Achnacarry, and the crowd broke into applause as the hearse was driven past in a final tribute to the hugely popular former MP.
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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