Data centres are being built all over the world, especially in the US, and people in Scotland using AI tools will not necessarily being using servers in Scotland.
However, many more data centres are expected to come to Scotland in the near-future, including a massive AI industrial park near Irvine in Ayrshire which was confirmed last month.
"If we had to supply all that with tap water, then that would be a real concern," Mr Lindsay said.
"These figures are very significant," said Prof Ana Basiri, director of university's Centre for Data Science and AI.
"There is a huge amount of carbon dioxide emissions and water use related to data centres that we often forget about because it is not a very visible thing," she said.
Many data centres are privately funded by US tech giants, such as Google and Microsoft, and major investment firms.
But most current owners do not share data about their environmental impact, something Prof Basiri said needed to change.
She added: "We can't really measure this because, of course, there is not necessarily a big mandate from the government to report on the detail of the energy or water use of data centres or other big tech companies that exist and that's a massive challenge."
Prof Basiri said one way to ensure that data centres were more sustainable would be to set carbon targets for companies and impose tax penalties for exceeding them.
The academic said the power used by an AI tool, such as ChatGPT or Google's Gemini, was about 13 times higher than a simple Google search.
She said ordinary people could play their part by considering their "AI footprint".
Prof Basiri added: "For example, reducing the number of times we go to these AI chatbot systems when a Google search would be efficient or considering how you use image generation, or what you attach to an email."
The UK is already thought to be the third-largest nation for data centres behind the US and Germany.
The UK government has made clear it believes data centres - which have been designated critical national infrastructure alongside the emergency services and healthcare systems - are central to Britain's economic future.
Despite concerns, Scotland has also been touted as a prime location for the development of "green" data centres.
This is because of its cool climate, abundance in renewable energy, and efficient grid.
OpenAI, the owner of ChatGPT, said it gives "considerable thought" to supporting sustainability efforts and "water-positive" goals.
The company said it had several global projects under way in this area.
This included a data centre in Norway which will "run entirely on renewable power" and is "expected" to use closed loop systems.
It added that it believes AI will also be "instrumental" in tackling climate change by "accelerating scientific discovery".
A Scottish government spokesperson said: "Alongside Team Scotland partners, the Scottish government is supporting initiatives to transform Scotland into a global centre for AI – driven by our capacity for renewable energy generation, strong local tech ecosystems and easy access to local talent and world-class academia.
"However it is vital that the sector grows sustainably in a way which doesn't impact on Scotland's natural resources or net zero ambitions."
They added Scottish Water was a statutory consultee on all data centre planning applications.
The spokesperson concluded: "Developers are encouraged to adopt measures such as 'closed loop' water systems, which seek to reuse water in data centres and minimise demand or use sustainable alternatives such as the use of treated final effluent as a sustainable water source."