The Home Secretary is understood to have concluded that altering the way that the law is written would have little practical effect.
Insiders say that she also accepts that the treaty, which was introduced in 2003, is not unbalanced and that critics’ accusations about flaws in the legislation are largely misplaced.
Mrs May’s decision follows the publication last year of a government-commissioned report on extradition law by the former Court of Appeal judge Sir Scott Baker.
It found that the “widespread perception” that arrangements with the US were unfair was “not justified” by the facts.
Despite the conclusions, a series of high-profile cases, including that of London computer hacker Gary McKinnon, have continued to prompt calls for reform.
The Home Secretary, whose party joined criticism of the legislation before the election, has concluded, however, that Sir Scott’s findings have shown that the law does not need significant changes.
Sources say that ministers acknowledge that they will have to “take a few hits” politically because of the decision, but that they feel bound to accept the former judge’s verdict because of the detailed way in which he conducted his analysis of the law.
The most crucial finding in Sir Scott’s report was that although different language is used in the legal tests applied by British and American courts, the hurdle that prosecutors must clear to secure extradition is equally high in both countries.
He also pointed out that while the UK has refused extradition requests from the US, all British requests have been approved by the American authorities and that the overall numbers being extradited from this country were not disproportionately high.
Sir Scott also concluded that even if a “forum” test had been applied in British courts to decide whether suspects should be tried in the US, as supporters of reform want, none of the extraditions that have so far taken place would have been halted.
Mr McKinnon, 45, an Asperger’s syndrome sufferer, is fighting extradition to the US over charges that he hacked Pentagon computers in 2002.
His legal team argues that his mental condition could lead to his suicide if he were sent to the US.