Turnbull government cabinet minister Darren Chester completed the purchase of an investment property on a taxpayer-funded trip to Melbourne in which he also attended the Australian Open tennis and a soccer match.

Stood aside Health Minister Sussan Ley's frequent taxpayer-funded trips to the Gold Coast, where she bought an $800,000 investment property, have reignited debate about whether politicians' entitlements are too generous and whether the lines between personal and private business are too blurred.

According to Mr Chester's register of interests, he purchased a two-bedroom unit in Ivanhoe, a leafy suburb in north-east Melbourne, while on official business on January 27 2016. A spokeswoman said this was the date of settlement for the property and that Mr Chester collected the keys to the unit on this date.

At the time Mr Chester, now the Minister for Transport and Infrastructure, was the assistant minister for defence.