The figures come days after the plan aimed at deterring migrant arrivals on small boats from northern Europe became law following months of parliamentary wrangling.
Rwanda has "in principle" agreed to accept 5,700 migrants already in the UK, the interior ministry revealed late Monday.
Of those, 2,143 "can be located for detention" before being flown there, according to the ministry.
Law enforcement agencies will find the remainder, Health Secretary Victoria Atkins said Tuesday when asked about the 5,700 earmarked for deportation.
"The expectation is that we remove that group of people... by the end of the year," she told Sky News television.
"If somebody doesn't report as they should do... They will be found."
Migrants who arrived in the UK between January 2022 and June last year are liable to have their asylum claims deemed inadmissible and be removed to Rwanda, the interior ministry said.
More than 57,000 people arrived on small boats after trying to cross the Channel during this 18-month period, according to official statistics.
The figure underlines the scale of the challenge trying to stem irregular arrivals, and the limits of the government's contentious plan to send some of them to Rwanda.
Under the scheme—set to cost UK taxpayers hundreds of millions of pounds—their asylum claims will be examined by Kigali.
If approved, they will be allowed to stay in Rwanda and not return to the UK.
Rwanda, home to 13 million people in Africa's Great Lakes region, lays claim to being one of the most stable countries on the continent and has drawn praise for its modern infrastructure.
But rights groups accuse veteran President Paul Kagame of ruling in a climate of fear, stifling dissent and free speech.
UK lawmakers last week passed the Safety of Rwanda Bill, which compels British judges to regard the nation as a safe third country.
It followed a UK Supreme Court ruling last year that said sending migrants on a one-way ticket there was illegal.
The new law also gives decision-makers on asylum applications the power to disregard sections of international and domestic human rights law.
UK opposition parties, UN agencies and various rights groups have criticised the flagship policy of Prime Minister Rishi Sunak's Conservative government.
He said last week that deportation flights are expected to begin within 10-12 weeks.