Sir Keir Starmer is planning to establish a series of "return hubs" overseas for rejected asylum seekers, with Kosovo among the countries being considered.
The western Balkan nation appears on a shortlist of nine countries identified by ministers and officials as potential destinations for these facilities.
While no formal discussions have begun with any country, the Government is understood to be seeking progress on these plans before hosting Western Balkans leaders in London this autumn.
The shortlist includes Serbia, North Macedonia, and Bosnia-Herzegovina, alongside Kosovo, plus several non-European nations that ministers want to approach.
Keir Starmer is considering sending Channel migrants to Kosovo
PAMinisters had initially hoped Albania would host one of Britain's return hubs but Prime Minister Edi Rama ruled this out last week.
Government sources have said Kosovo is a "plausible" location because it sits on one of the main routes used by illegal migrants travelling towards the European Union.
According to the Foreign Office, nearly 22,000 illegal migrants used the western Balkans route to enter the EU last year.
Kosovo's President Vjosa Osmani has indicated her country would be "open" to discussions about hosting one of Britain's return hubs.
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She said: "There's been no formal talks with the UK on this issue. It hasn't been raised so far.
"We would be open to discussing it, however, I can't say more than that because I don't know the details. I cannot give an answer on a request that hasn't been made so far."
The UK would likely argue that migrants passing through countries hosting return hubs had opportunities to claim asylum in "safe" countries but chose not to.
Starmer faces mounting pressure over rising numbers of migrants arriving in small boats.
Kosovo's president, Vjosa Osmani, has indicated her country would be 'open' to discussions
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A record 13,573 migrants have crossed the Channel so far, representing a 37 per cent increase compared to the same period last year.
More than 3,000 migrants entered the EU after travelling through the western Balkans in the first four months of this year, including 804 in April, according to the EU's border agency, Frontex.
Kosovo, one of Europe's poorest nations, has a population of about 1.6million and is bordered by Serbia, Montenegro, North Macedonia and Albania.
Any agreement with Britain would require payment for each failed asylum seeker relocated to Kosovo.
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