Nigeria's performance at London 2012 was the worst in at least 20 years, analysts say.
It fared worse then many other African countries, including South Africa.
Mr Jonathan had raised the issue at a cabinet meeting in the capital, Abuja, Mr Maku said.
"He believes that what this nation needs at the moment is to take a sober look at what has happened and indeed change the scenario... to return the sporting sector to its past glory," Mr Maku added.
Nigeria is Africa's most populous country and sees itself as a superpower on the continent.
It spent more than $13m (£8m) on the Olympics.