Duncan Campbell and Ciara Phillips, who still live and work in Glasgow, as well as Tris Vonna-Michell, all attended Glasgow School of Art. They are in the running for the £25,000 prize, now in its 30th year, along with London-based artist James Richards.
If Campbell, Phillips or Vonna-Michell win they will be the seventh artist with Scottish links to take the prize - often associated with critical controversy - since 1996.
Last night Campbell, a Dublin-born artist whose video and film work tackling colonialism and its consequences represented Scotland at last year's Venice Biennale, said he was delighted to be shortlisted.
Phillips, an Ottawa-born artist who works with print and transforms galleries in workshops, and who was nominated for a show in London, said: "It has been a surprise but a nice surprise.
"What is really nice is that there is the opportunity to make a show at Tate Britain. It is good to be recognised for the work you have done - I know two of the other shortlisted artists very well, and I don't feel it is competitive at all. This is a very nice stage to be at."
Vonna-Michell is in the running for a solo exhibition in Brussels and he makes spoken-word live performances and recordings.
Lizzie Carey-Thomas, curator of the Turner Prize show, said: "I thi nk the shortlist just confirms that Glasgow is one of the most vibrant centres for the contemporary arts, that it is a good place for artists."