President Anastasiades and President Akinci have been invited to attend the World Economic Forum in Davos to informally discuss security and guarantees.
They will also meet heads of state, international institutions and investment funds to find ways of funding a Cyprus settlement.
President Anastasiades has heard that Turkey is prepared to hold comprehensive discussions on guarantees, Cyprus Weekly reports. South Cyprus and Greece want to abolish the existing guarantees system, while the UK is open to discussion on the matter.
Initially, Ankara sent a message to Nicosia that it was open to discussion on the matter of guarantees. It then suggested that guarantees could be non-military and last for a specific time period.
President Anastasiades, while willing to discuss security issues, has said he will not permit any interventions by Turkey over decisions regarding a reunited Cyprus.
It is also possible that President Anastasiades and Turkish Prime Minister Ahmet Davutoglu might hold an informal meeting, as they did last year.
The main reason for Anastasiades and Akinci go to attend the World Forum in Davos is to meet with important players on the political and financial scene.