According to the book in May 2015 the Swiss foreign affairs office (EDA) asked Blatter, then boss of football's world governing body Fifa, to help them prevent Burundi's controversial president Pierre Nkurunziza from running for a third term in office by offering him a job in football.
EDA spokesman Stefan von Below confirmed the news to The Local, saying: "The EDA confirms that there was a contact between State Secretary Yves Rossier and Mr. Joseph Blatter. The intention was to contribute to a peaceful solution in order to prevent the current crisis in Burundi.".
The ministry would not comment on Blatter's claim, reported by Blick, that the request came from the US.
Switzerland plays a key role in international relations with Burundi, heading up a UN commission trying to broker peace in the unstable area.
"Switzerland's commitment to peace and stability in Burundi has been longstanding," the ministry told The Local.
It added that it contributed to the drafting peace agreements for the country and has continued to support Burundi "with its instruments of peace policy, development cooperation, humanitarian aid as well as through diplomatic channels."
Speaking to Blick, a second spokesman said it was “not unusual to call on non-diplomats if their experience and networks can help solve problems”.
But the ministry told The Local they "never asked president Nkurunziza not to run for the office of president again."
Blatter's mission came just days after a failed coup by General Godefroid Niyombare against Nkurunziza in May 2015, said the paper.
Blatter, too, was unsuccessful. Born-again Christian Nkurunziza turned down his offer to become ambassador for football in Africa saying he was “chosen by God to rule Burundi,” said Blick.
Nkurunziza was elected in 2005 in the first democratic elections since the start of the Burundi civil war.
But since then his presidency has become regarded as increasingly authoritarian, with reports of press harassment, political repression and violence.
Despite the Burundi constitution limiting a president to two terms in office, in April 2015 Nkurunziza announced he would run for a third term, prompting months of protests and violence and the failed military coup. He was elected in July.
A few months after his mission Blatter was himself thrown off his perch as president of Fifa due to an ongoing corruption scandal.
He led Fifa for 17 years, winning a fifth term in office before he was suspended in October 2015 over an unauthorized payment to Uefa boss Michel Platini. He was later banned from football for eight years, later reduced to six.
Blatter's authorized biography, out in German today, was written by former Fifa spokesman Thomas Reneggli. An English translation is due out in June.