Chief Medical Officer Catherine Calderwood has also played down suggestions that Scotland is coping better than south of the border with the virus, insisting the current lower levels are likely to be down to a time-lag.
There have been more than 700 cases in Scotland and the chief medical officer said this will keep rising in the short-term before the impact of the lockdown is seen.
In London the Excel centre has been set up as a makeshift hospital with 4,000 beds to be available in it, while the NEC in Birmingham is also reportedly being considered for a major "field" hospital.
Asked is something similar is being planned in Scotland, Dr Calderwood told BBC Radio Scotland's Good Morning Scotland show: "We are, absolutely.
"We have had quite detailed discussions very recently and I know that there are sites being considered in Scotland this week."
There have been 22 deaths in Scotland which is proportionately lower per head than England where there have been 465 fatalities.
But the chief medic warned that people can be ill for two-three weeks before being hospitalised.
She added: "I'm worried that these low deaths are actually just because we haven't had the virus in Scotland for as long as as they've had it in England.
"There hasn't been enough time for people to get more unwell and hospitalised and then onto that stage where they are needing intensive care. This is probably just a time issue, rather than it being a lower death rate per se.
She also urged NHS staff to be selective about how and when they use protective equipment mid concerns of shortages.
"I'm hearing from my colleagues and this makes me very uncomfortable to send people to work on the frontline when they're worried that the masks in particular will run low or run out,” she added.
"We're also hearing people are using masks where actually they don't need to be using them and that is depriving somebody else who does need the mask.
"So we're asking people to be clear what protective equipment you do need and only use it if you do need it.
There's a global shortage of protective equipment in part because the factories in China where most of these are made have been shut down for so many weeks.
"So, this is not a Scottish problem, it's a across the world. We have new supplies that I released earlier this week which were from one of our supply chains and the distribution model we are changing very rapidly."