Attempts to behead a statue commemorating James Cook in a Melbourne park have reportedly occurred overnight on Tuesday, launching police investigations.

It is believed two alleged offenders attended Cooks' Cottage at Fitzroy Gardens just east of the CBD at around 2am on Tuesday morning, the pair allegedly spray painting "various anti-Cook comments" at the site, a Victoria Police spokesperson said.

A statue of Cook was also damaged "by what appears to be an attempt to remove the head".

City of Melbourne Lord Mayor Nick Reece said the Council's Security Control Centre witnessed the statue and cottage being damaged and made the vandals aware they were being recorded before they left the scene.

The same site was targeted almost exactly 12 months ago.

On February 26 2024, vandals cut down the statue of the colonial figure.

The bronze monument was reinstalled after being repaired earlier this month.

"Defacing or damaging city assets will not be tolerated – and Council is taking proactive measures to stop damage to our statues in its tracks," Mr Reece said on Tuesday.

"Our security team observed Cooks Cottage and the Captain Cook statue being damaged early on Tuesday morning – and implemented measures that prompted offenders to leave the scene.

"While there are a range of views on statues and memorials, each time a monument is damaged, it's ultimately the ratepayer footing the bill – and that is unacceptable."

The Cottage was built by Cook's father in England in the mid 18th century and shipped to Australia in 1934 where is was reassembled in East Melbourne, according to Visit Victoria.

According to reports, the paint left overnight has been cleaned.

A number of colonial-era monuments around the country were targeted earlier this year in the period surrounding January 26.

This included a memorial honouring one of Melbourne's founders, John Batman, at Queen Victoria Market, being damaged on the long weekend.

It followed a string of similar incidents in previous years.