Gabriel, who is also vice chancellor and leader of the Social Democrats (SPD) who share power with Chancellor Angela Merkel's conservatives, plans to take a small delegation on a three-day visit, said the sources.
A spokeswoman for the ministry said a visit to Iran was being considered but she declined to say when it would happen.
"There is a great interest on the side of German industry to normalize and strengthen economic ties with Iran - even more so after the nuclear agreement with Iran," said the spokeswoman.
German companies, from Volkswagen to Siemens and thousands of smaller family-owned firms are lining up to take advantage of the Iranian market.
German industry associations said on Tuesday exports to Iran could quadruple in the next few years as a result of the deal.
The head of the BDI industry association predicted exports could jump to more than 10 billion euros in the medium term from 2.4 billion euros last year, seeing the car, chemical, healthcare and renewable energy industry as potential winners.
During the years of sanctions against Iran, German exports to Iran fell from a high of 4.4 billion euros in 2005 to 1.8 billion euros in 2013.
On a trip to Beijing, Gabriel described the deal as a "historic breakthrough", adding it was now time to talk about a change in the relationship between Iran and Israel.
The 60-strong delegation will include representatives of big German industrial companies such as Linde and Siemens, Amir-Hussein Zamaninia, Iran's deputy oil minister for commerce and international affairs, has said.
Gabriel, who is also Germany’s vice chancellor, will meet with President Hassan Rouhani, Minister of Petroleum Bijan Zangeneh as well as Iranian ministers of trade and energy and the central bank governor.
"We expect to see a big increase in trade, especially in German sales of capital goods," the Deutsche Welle website quoted Michael Tockuss, chief executive at the German-Iranian Chamber of Commerce, as saying.
According to the German Foreign Ministry, bilateral trade grew by 27% to 2.7 billion euros ($3 billion) in 2014 because of the sanctions relief.  
Tockuss said trade volume could easily rise to double-digit billions in the longer term given the size of the two countries’ economies. Germany had a GDP of 3.27 trillion euros in 2014 in terms of purchasing power parity versus Iran's $1.18 trillion.
German companies have been exploring opportunities in Iran for months amid expectations that the sanctions would be lifted.
"Airliners flying to Tehran have been full of German businesspeople for weeks or months. The mood has brightened considerably during the past year," Tockuss said.
Iran expects to resume its exports of crude oil, agricultural products and petrochemicals especially from a 350 million-euro complex which is being built by Linde at the Imam Khomeini Port.
The Germans hope to step up industrial equipment and machinery sales to Iran given the size of industries in the Middle Eastern country.
Iran has a massive oil, gas and petrochemical sector. It is the biggest producer of cars in the Middle East. It also manufactures aircraft, a wide range of agricultural products, cement and other construction materials.
"Construction machinery, chemicals, food processing, renewable energy equipment - those are some of the areas I think are especially promising for German industry," said Sasan Krenkler of Krenkler & Partner, a business consultancy specialized in helping German companies enter Iranian markets.