The federal government will discuss the offer at a meeting on Friday and is expected to present it to the EU in Brussels on Tuesday, broadcaster RTS reported.
The goal is to help front-line countries Greece, Italy and Hungary in dealing with the influx of thousands of asylum seekers, as well as Germany and Sweden, which have ended up with the bulk of them.
Swiss President Simonetta Sommaruga told reporters at a meeting of German-speaking heads of state in Liechtenstein on Thursday that there was no national solution to the asylum issue but only a pan-European one.
The federal government has thus far avoiding discussing the refugee issue, given that most asylum seekers have been heading to Germany and Sweden, giving Switzerland a wide birth.
Voters in Switzerland last year approved capping immigration from the EU in defiance of a freedom of movement agreement that Bern signed with Brussels.
But the dynamics of the refugee crisis changed this week after Germany, which expects to take in one million refugees this year, temporarily closed its borders after being overwhelmed by migrants.
Austria and Hungary followed suit and now Slovenia and Croatia have put in similar controls.
Police clashed with refugees on Wednesday in Hungary, where the state has erected a barbed-wire fence on its border.
Donald Tusk, president of the European Council, called an emergency summit for next Wednesday to talk about instituting an EU quota system, which has been vigorously opposed by Eastern European countries.
The Swiss government, meanwhile, will also discuss the possibility of humanitarian aid to help non-governmental organizations (NGOs) active in Iraq or Syria, RTS reported.
A sum of between 50 million francs and 100 million francs has been proposed, the broadcaster said.