Former independent MP Rob Oakeshott tried to convince Liberal MP Malcolm Turnbull to become a minister in a Labor-led minority government ''rainbow cabinet'' he envisaged while negotiating with Julia Gillard to back her into the prime ministership.

The revelation is made in Mr Oakeshott's forthcoming memoir, The Independent Member for Lyne, which gives insight into the extraordinary 17-day period after the 2010 election, when a hung parliament meant that Oakeshott, and his fellow independent were left to decide whether Australia would have a Labor or a Coalition government.

Tried to convince Malcolm Turnbull to become a minister: Rob Oakeshott enjoys some beach time with his family. Credit:James Brickwood

Mr Oakeshott recounts that during that period he had many private conversations with Mr Turnbull and raised with him the idea of joining the cabinet of a Gillard-led minority government.

''I tell him I would only consider being a minister in a Labor government if there were others who joined me,'' Mr Oakeshott writes of the now-Communications Minister.