Germany wants tougher limits on hunting the animals, but Botswana says it has too many of them.
Earlier this year, Germany's environment ministry suggested there should be stricter limits on importing trophies from hunting animals.
Botswana's President Mokgweetsi Masisi told German media this would only impoverish people in his country.
He said elephant numbers had exploded as a result of conservation efforts, and hunting helped keep them in check.
Germans should "live together with the animals, in the way you are trying to tell us to", Mr Masisi told German newspaper Bild. "This is no joke."
Botswana is home to about a third of the world's elephant population - over 130,000 - more than it has space for.
Herds were causing damage to property, eating crops and trampling residents, Mr Masisi said.
Botswana has previously given 8,000 elephants to neighbouring Angola, and has offered hundreds more to Mozambique, as a means of bringing the population down.
"We would like to offer such a gift to Germany," Mr Masisi said, adding that he would not take no for an answer.
Botswana's Wildlife Minister Dumezweni Mthimkhulu last month threatened to send 10,000 elephants to London's Hyde Park so British people could "have a taste of living alongside" them.
In March, UK MPs voted to support a ban on importing hunting trophies, but the legislation has further scrutiny to pass before becoming law.
This reminds me of the story during colonization. The Europeans went to Africa and said you guys need to plant crops like we do. So the Europeans planted crops, they grew, and then the hippos came and ate it all.