Connecticut-based hedge fund Gramercy purchased the defaulted debt at a discount in 2008 after other bondholders failed to reach a deal.
Peru's finance minister said the government would oppose any legal action outside its borders.
Purchasing defaulted bonds on the cheap to make a profit in a settlement is a common hedge fund tactic.
The South American country defaulted on the $5.1bn (Â£3.33bn) in bonds in the 1980s.
Gramercy has threatened to bring a claim against Peru under a tribunal system established in a US-Peruvian trade deal.
This type of action has been called "predatory" by groups in favour of sovereign debt relief plans.
Argentina has been engaged in a prolonged court battle with hedge funds over bonds it defaulted on in 2005.
This week Peru has played host to meetings of the World Bank and International Monetary Fund (IMF).  Among the topics discussed was how to help country's restructure debt after a default to avoid drawn-out court battles.
A US hedge fund has threatened to sue Peru over bonds issued by the country's former military regime.