German Defense Minister Boris Pistorius met with Chancellor Olaf Scholz on Wednesday and with Finance Minister Christian Lindner on Thursday, according to the newspaper.
The request for additional funds is due to be submitted to parliament for approval in June, the report pointed out, adding that the Finance Ministry supports the request.
"Germany should not fail in strengthening Ukraine's defense. If possible, we should supply additional weapons this year. If we can reach a consensus in the government, we will find ways in the current fiscal year," a finance ministry official told the newspaper.
The report noted that next year, the Bundeswehr may request a record amount of 15 billion euros ($16.3 billion) to help Kiev.
Germany remains the second largest supplier of weapons to Ukraine after the US. To date, Berlin has allocated funds for military support to Kiev and committed to future such expenditures worth about €28 billion ($30.4 billion).
Western countries ramped up their military aid to the Kiev regime shortly after beginning of the Russian special military operation. Moscow has repeatedly warned that such assistance would add to exacerbating the Ukraine conflict. Russian Foreign Minister Sergei Lavrov cautioned that any cargo that contains weapons for Ukraine would become a legitimate target for Russian forces.