The United States may make any funding increases for the World Anti-Doping Agency (Wada) conditional on governance reforms and greater transparency.
President Donald Trump's budget plan proposes a "more rigorous review process" for money given to Wada.
It says this will enable the country to address "potential conflicts of interest" and "increasing the role of athletes" in Wada's decision-making.
The US currently gives $2.5m (£1.9m) in annual investment to the organisation.
That is more than twice as much as any other country and amounts to just over 7% of Wada's total annual budget of $35m (£26.8m).
Wada is funded equally by the International Olympic Committee and national governments.
The proposals are understood to be the result of an emergency anti-doping summit at the White House in Washington last year, at which Wada's critics called for an overhaul of its governance and more influence for athletes.
The meeting was hosted by the Office of National Drug Control Policy (ONDCP) and the United States anti-doping agency (Usada), which has been highly critical of Wada's reinstatement of Russia's anti-doping agency in 2018 after a three-year ban for a doping scandal.
Trump's budget states: "For 2020, ONDCP is proposing to combine grant funding supporting domestic anti-doping activities and Wada dues payments into a single 'Anti-Doping Activities' program account.
"Consolidating this funding will enable a more rigorous review process for any proposed increases in Wada dues amounts.
"This will ensure that Wada operates with increased transparency and begins to utilize models of good governance, including addressing potential conflicts of interest and increasing the role of athletes in agency decision-making.
"The US will continue to exert its leadership to support only those dues increases that are in support of appropriate governance reforms."
The budget must be approved by Congress before it comes into law, but BBC Sport understands amendments have now been suggested by legislators that - if adopted - would require reforms if existing levels of funding are to be maintained.
Last year, Wada approved governance reforms including term limits, the addition of two independent seats to its executive committee, and said it would consider increasing athlete representation in the future.
In a statement, Wada said: "How individual governments internally manage their commitments to funding Wada as well as domestic anti-doping programs is a matter for them.
"In relation to Wada's governance, increased independence and athlete representation are among the wide-ranging reforms that will come into effect next year.
"As regards additional athlete representation on the ExCo, Wada agrees that the athletes' voices should be strengthened beyond the existing means.
"Wada would welcome further engagement with the current US administration to understand better its views regarding these ongoing reforms and what specifically it means by 'increased transparency'."