The equipment is made by Krauss-Maffei Wegmann and Rheinmetall
Qatar aims to buy 118 more Leopard tanks from Germany before the soccer World Cup championships in 2022 for several billion euros, a German newspaper reported on Sunday.
It also plans to buy 16 tank howitzers, Bild am Sonntag reported citing government sources in Qatar.
The equipment is made by Krauss-Maffei Wegmann and Rheinmetall. Spokesmen were not immediately available for comment in Qatar or at Krauss-Maffei or Rheinmetall.
Chancellor Angela Merkel's government approved the purchase of 62 Leopard tanks and 24 howitzers in the spring.
Arms exports are a sensitive issue in Germany given the country's Nazi past and the role arms makers like Krupp played in fuelling wars in previous centuries.
Peer Steinbrueck, Merkel's opposition Social Democrat (SPD) challenger in September's election, has attacked her government for letting arms exports surge and said he would end that if his centre-left alliance wins.
After World War Two, West German and united German governments placed tight restrictions on arms exports, especially to regions where there were armed conflicts or which had poor human rights records.