The 63-year-old former Kingfisher Airlines boss had filed the application seeking "leave to appeal" in the High Court on February 14 against his extradition order, which was signed by UK Home Secretary Sajid Javid.
"The application for permission to appeal was refused by Mr Justice William Davis on 05/04/2019," said a spokesperson for the UK Judiciary.
"The appellant (Mallya) has five business days to apply for oral consideration. If a renewal application is made, it will be listed before a High Court judge and dealt with at a hearing," the spokesperson added.
Mallya's "leave to appeal" application had been put before Justice Davis, who was to make a decision on the basis of papers submitted as part of the appeals process. Now that the "judge on papers" application has been rejected by Justice Davis, Mallya has the option to "renew his application for permission to appeal" by this Friday.
"If he (Mallya) does so (applies for renewal), there will be an oral hearing at which the Administrative Court (High Court) will consider whether or not to grant permission to appeal," a CPS spokesperson said.
During the oral hearing, Mallya's legal team and the Crown Prosecution Service (CPS) - on behalf of the Indian government - will renew their respective claims for and against an appeal for a judge to determine if it can proceed to a full hearing.
While the rejection by the High Court on Friday doesn't mean that the appeal process in the case has come to an end, the latest decision does move the case one step further in favour of India in bringing back Mallya, who had fled the country in 2016.
Last Thursday, the embattled liquor tycoon said he is willing to curtail his "lavish" lifestyle to satisfy numerous Indian banks trying to recoup some of the nearly 1.145 billion pounds owed to them, a UK court was told.
The 63-year-old had been sanctioned an "ordinary living expenses allowance" of a maximum of 18,325.31 pounds a week, which he offered to cut down to around 29,500 pounds a month during a UK High Court hearing this week.
In a ruling in May last year, a UK High Court judge had refused to overturn a worldwide order freezing Mallya's assets and upheld an Indian court's ruling that the Indian banks were entitled to recover funds amounting to nearly 1.145 billion pounds.
Mallya, meanwhile, remains on bail after his extradition was ordered by Westminster Magistrates' Court in London in December last and signed off by UK home secretary Sajid Javid in February. He has since filed an application in the UK High Court seeking leave to appeal against that order.
(With additional information from PTI)