Spokesperson for Kern, Jürgen Schwarz, told reporters that the talks are expected to concentrate on securing the European Union's external borders.
Austria has promised to send 20 police officers to Hungary's border with Serbia, where around 30 asylum seekers a day are allowed to cross into a border ‘transit zone' where they can apply for asylum.
Around 1,400 people are waiting on the Serbian side of the border to be allowed across the EU border, according to the UNHCR.
Last summer Hungary built a fence over 100 miles long at its border with Serbia in a bid to hold back the flow of asylum seekers and migrants - mainly from the Middle East - crossing its border.
This summer the numbers of asylum seekers trying to enter Europe via Hungary has dropped significantly following the 'closure' of the so-called West Balkan route.
Earlier this week police in Austria announced they had finished preparations for building a possible 100 kilometre fence along its eastern border with Hungary after securing permission from hundreds of private landowners in the region.
The fence is part of the country's efforts to prepare for a possible repeat of last summer when thousands of asylum seekers and migrants arrived to Europe every day.
According to Hungarian media, around 30 and between 30 and 40 asylum seekers and migrants are estimated to cross the border into Austria every day.
At the meeting today - the first between the two heads of states - the leaders will also discuss the issue of returning asylum seekers from Austria to Hungary under the Dublin Regulation.
The regulation stipulates that asylum seekers can be sent back to the first EU country they enter. There are currently thousands of people who fall into this category in Austria and authorities hope to return them to Hungary.
Hungary has so far refused to accept returning asylum seekers, arguing that the first EU country they entered was Greece.
The return of asylum seekers to Greece was frozen last year, however, following a EU court ruling against it on human rights terms.