If the banks were to agree to such a settlement, it would allow the EU's antitrust chief Joaquin Almunia to wrap up his investigation as soon as this year and before his term as antitrust commissioner draws to a close in late 2014.
"Almunia wants decisions on the cases by the end of the year," said one of the sources familiar with the investigation.
The offer comes almost 18 months after the Commission raided a number of banks suspected of Euribor rate rigging. It later widened its investigation to other benchmarks.
The move signals that there is a prospect of reduced fines from Brussels in return for ending any activities that could lead price-fixing of Euribor, the euro interbank-offered rate, and its larger counterpart the London Interbank Offered Rate (Libor).
Many banks are reluctant, however, to settle with the Commission because they believe the charges are unfounded, they said.
If they resist and the Commission later finds them guilty of manipulation, they would face a fine equivalent to 10 percent of their annual revenue. That could rise to three times as much if individual banks are prosecuted for rigging three benchmarks. By settling, the fines would be reduced.
A spokesman for Almunia declined to comment on the prospect of any settlement.
Heavy penalties already loom in other regions. The United States and Britain will by mid-year levy more fines against those alleged to have been involved in interest rate rigging, sources close to the probe said.
U.S. and UK regulators have fined three banks to date - RBS, Britain's Barclays and Switzerland's UBS - a total of $2.6 billion for allowing traders to game Libor interbank rates in a global scam.
Earlier on Friday, Almunia said he had widened his investigation of suspected unfair fixing of lending benchmarks such as Euribor and Libor to interest rate products for the Swiss franc.
Euribor and Libor are the key gauges of how much banks pay to borrow from each other, and are used as reference points for swathes of financial products from Spanish mortgages to derivatives contracts sealed in London.
Both are set using interbank borrowing rates submitted by banks.
(Writing by John O'Donnell; Editing by Will Waterman)
By Foo Yun Chee