The Lego Foundation, the research arm of the Denmark- based plastic block-building toy company, has provided the university with 2.5 million pounds to fund a Lego Professorship of Play in Education, Development and Learning.
It has also provided 1.5 million pounds to support a play research centre in the education faculty, the BBC reported.
Last year, Cambridge University advertised for a doctor of chocolate to study how and why the substance melts.
The offer from the Lego Foundation, which owns 25 per cent of the toy firm, is currently "up for consideration" by the university's board, ITV News quoted a Cambridge spokesperson as saying.
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The General Board, in their Report on the Establishment of Certain Professorships, published in the Cambridge University Reporter yesterday, recommended the establishment of a Lego Professorship of Play in Education, Development and Learning from the start of the next academic year.
The successful applicant will also be a director of a new Cambridge research centre, which will investigate the role of play in education.
The Lego Foundation says it aims to "build a future where learning through play empowers children to become creative, engaged, life-long learners".