Several patrons of the Nelson Mandela Scottish Memorial Foundation (NMSMF) are backing the drive for the final £30,000 needed to build the tribute.
A total of £70,000 has already been raised and it is hoped the remaining sum will be pledged between the anniversary today and United Nations Nelson Mandela International Day on 18 July.
Brian Filling, chair of the NMSMF and honorary consul for South Africa in Scotland, was instrumental in bringing Mr Mandela to Glasgow in 1993 to accept the freedom of the city.
He said: “Fundraising so far has included major events but also individual donations and initiatives like kilt walks and birthday and retirement donations.
“We have made major strides in setting up an education programme for schools and with this new five-month drive, we will be within shouting distance of at last making the statue a reality.
“While Mr Mandela was in prison, many ordinary people in Scotland organised and acted to make sure the world would know about him and the fight against Apartheid.
“That’s why we want today’s generation to join us in raising the funds to make this statue one that they can see as theirs - a ‘people’s statue’ that they can call their own and to remind future generations of the key part Scotland played in taking action for human rights and challenging racism, and on taking action for a better world.”
Glasgow was the first to offer Mr Mandela freedom of the city, which paved the way for 2,500 mayors from 56 countries to eventually sign a declaration to the UN in 1981 demanding his release.
The statue would be placed at Nelson Mandela Place in the city centre, renamed in 1986 because it was home to the Glasgow South African Consulate.
It is also close to George Square, where he addressed crowds during his visit seven years later.
Sir Alex Ferguson, a patron of the campaign who met Mr Mandela on three occasions, said: “Nelson Mandela was special. An example for the world to follow. For decades the ordinary people of Glasgow have played a terrific role in the anti-apartheid movement.”
Denis Goldberg, who stood trial with Mr Mandela in 1964 and spent 22 years in prison, is also a patron of the campaign.
He said: “I have very fond memories of Glasgow and its people from my many visits to Scotland following my release after 22 years in prison. The city’s support for our just cause will never be forgotten by us South Africans.”