Academy chains are being encouraged to set up selective schools under government plans that include expanding grammar schools in England.
Separate units for high-ability pupils are also being encouraged within their existing chains of schools.
Schools standards minister Nick Gibb told academy bosses new selective schools would bring more choice and flexibility to the education system.
The National Union of Teachers said the majority of children would lose out.
And the Association of School and College Leaders (ASCL) said this undermined the current consultation on increasing selection in the education system if ministers were already pitching the idea.
Mr Gibb was speaking at a conference organised by Academy Ambassadors, an organisation that supports academies bringing skilled businesspeople on to the boards of academy trusts.
He said the government’s proposals were “asking how some existing non-selective schools, including academies, could become selective – if they wish”.
He said: “The consultation also proposes entirely new selective schools being established as free schools, to widen choice, to bring more flexibility, and to challenge those areas of the country where too few pupils are entered for the EBacc combination of core academic GCSEs.
“Some of the schools in your trust may wish to introduce selection by ability.
“Your trust may consider establishing a new selective free school or you may look to expand using the routes that are already available.”
He added: “The consultation will also look at how we might encourage multi-academy trusts to establish single centres in which to educate the most able pupils.”
Mr Gibb said this was already possible for academies through the non-selective admissions process, as the most able were identified after they had been admitted to an individual school.
Kevin Courtney, general secretary of the National Union of Teachers, said: “Once again ministers are demonstrating that they have the wrong priorities for education, instead of focusing on how we can deliver a world-class education for all pupils in all schools in England.
“The government is pursuing its plans for a costly restructure of the school system which all education experts oppose and in which the majority of children will lose out.”
Malcolm Trobe, ASCL acting general secretary, said: “The evidence indicates that increasing selection will not have the same effect as the policy imperative, which is to improve social mobility and improve overall education quality in this country.
“The most appropriate step now is to collate evidence and await the outcomes of the consultation before taking any decisions.”
He also suggested the special units for the most able pupils within chains appeared to seek to create an absolute academic elite.