In this context, that is not enough to be interesting to most banks that accept non-resident foreigners. They want between 100x and 1,000x that amount. As an ordinary retail customer, it's not worth the hassle to most banks. The costs of opening and maintaining the account are greater than the income they can expect to generate. However, you can try speaking with ING, Keytrade, and
BNP Paribas in Belgium; Intesa and UniCredit in Italy; and Santander, Caixa, and Banco de Sabadell in
Spain. There might be others worth speaking with. But they will probably say no, unless you can show that you have close ties to the country, plan to use the account regularly (salary payments,
investments), or relocate to the country.
However, you can open accounts with
Swissquote,
CIM Banque, Flowbank, and
Dukascopy in Switzerland. Swissquote isn't good if you need the account to make third-party bank transfers, but you can quite easily get a Swiss
credit card if you need a local card.