ATHENS—Greece is close to a deal with its private-sector creditors to restructure the country's debt, Finance Minister Evangelos Venizelos said Tuesday, amid recent signs that the two sides were narrowing their differences.

"We are close to a deal, I believe that, because I have personal knowledge of the negotiations... and I know it is do-able," Mr. Venizelos told a gathering of business and labor leaders.

Recent media reports have described the talks as advancing after the two sides reached a deal to apply U.K. law to new bonds issued by the Greek government, and agreed on other details. And last Friday, the government and the creditors—meeting in Paris—issued a joint statement saying they had made progress.

In late October, euro-zone governments called on Greece to secure a 50% write-down in the debt held by private creditors as a condition for a €130 billion bailout package for the country.

But they said the participation of private investors should be voluntary, in order to avoid payouts under credit default swaps that might inflict further damage on the currency area's fragile financial system.

If an agreement is reached, about €200 billion of debt held by private investors will be cut in half and save Greece some €5 billion a year in debt-servicing costs.

In his remarks, Mr. Venizelos said that separate negotiations on the new €130 billion bailout would begin on Jan. 16 when a visiting troika of European and International Monetary Fund officials return to Athens to hash out the details of the new program.

But Mr. Venizelos also stressed that Greece must step up the pace of its structural reforms—something being demanded by the so-called troika—after months of delays.

Among the reforms Greece is expected to push in the weeks ahead will be efforts to overhaul its tax system and crack down on chronic and widespread tax evasion.

In an effort to catch tax evaders, the government has promised a sweeping overhaul of the tax system, and has been negotiating a deal with Swiss authorities aimed at taxing billions of euros worth of bank deposits thought to be held by Greek tax evaders outside the country.

According to some estimates, Greek residents hold as much as €200 billion in Swiss bank accounts, much of that is thought to represent cases of tax evasion by wealthy Greeks.

Mr. Venizelos said that Greece's parliament would ratify the bilateral deal with Switzerland on Wednesday.

.wsj.