The Moray MP says he wants the First Minister to explain to Scots why another vote on leaving the UK is “essential” to the country’s recovery from the pandemic.
The SNP has set out a roadmap to independence in recent weeks. Ms Sturgeon says a Nationalist majority at the Holyrood election in May will be a mandate for another vote on leaving the UK.
Mr Ross has said he would expect Scotland's top law officer, the Lord Advocate, and Holyrood's Presiding Officer to challenge Scottish Government plans to press ahead with a referendum without agreement from Westminster.
The Tory leader made a flagship speech on Monday in response by the recent publication of the SNP's 11-point road map to independence that set out plans for a referendum in the event of pro-independence majority of MSPs at the Holyrood election in May.
The Tory leader said politicians had a "come together and focus on the national interest" during the Covid-19 pandemic, which should be focused on vaccine rollout and our recovery from the pandemic.
Ms Sturgeon has indicated she would publish legislation setting out the “terms and timing” of another vote on the leaving the UK before the Holyrood vote in May.
But Mr Ross said: “We are going to need to have a Covid election.
"And my party will fight that election as hard as we have ever done.
“We will match the SNP’s renewed threat of indyref2 this year, with a renewed push to stop them in their tracks, just as we did in 2016 and every year since.
“The SNP are not holding back. They’ve taken the gloves off and they’re going full-throttle for indyref2 right now, which is why I am challenging Nicola Surgeon to a debate this month on Scotland’s future.
“If she believes that this referendum plan is an essential part of Scotland’s economic recovery from coronavirus, then she should explain it to the Scottish people.
“So let’s not wait for the election.
“Nicola Sturgeon, SNP leader, let’s you and I debate our respective positions right now."
It is expected that any debate would be televised live.
SNP deputy leader Keith Brown claimed his party was “determined” to give people a choice in how they were governed.
He said: "This is a patently ridiculous and deeply hypocritical attack from a party more interested in desperate soundbites than working constructively to overcome the Covid-19 pandemic.
“The Scottish Government is absolutely focused on tackling the pandemic, which remains everyone’s top priority, and paused work on independence last year at the start of the Covid crisis – unlike the Tories who disgracefully ploughed ahead with Brexit in the middle of the pandemic.
“Just yesterday, Alister Jack was attacking the First Minister's commitment to keeping the public updated and informed through daily public health briefings – now his colleague is claiming the opposite. They're clearly in panic mode, but people in Scotland will see right through this bizarre outburst.
"While Douglas Ross carps from the sidelines, the First Minister will continue to be fully focused on helping steer the country through this crisis."