The retired cricketer was hosting a party at his village mansion in northern England late last month, when the valuables were taken, according to British tabloid newspaper The Sun.
His wife Kathy, 49, discovered the theft after guests had departed, it said.
North Yorkshire Police confirmed they were investigating a "high-value" theft from a property in the area, but refused to confirm whether it was from the home of the England cricket hero.
Two people were arrested earlier this week but were released on bail pending further inquiries, a police spokesman said.
Botham, 49, now a television sports presenter, is considered one of the greatest all-rounders ever to play cricket. In 102 tests for England, he scored 5,200 and took 383 wickets.