Suleiman met with Cypriot President Demetris Christofias in Beirut to discuss the natural resources that may lie offshore.
"We have decided to increase the frequency of coordination and cooperation to reach an agreement about the principles and mechanisms which will allow both our countries to extract this wealth," the Lebanese president was quoted by The Daily Star newspaper as saying.
Beirut aims to have an international auction for natural gas tenders Feb. 1. At least 40 countries are said to have expressed interest in the bidding.
Cyprus has an estimated 12 trillion cubic feet and has agreements with Egypt and Israel to examine transboundary hydrocarbon deposits.
Lebanon has called on the United Nations to help determine its maritime border given disputes with Israel. Lebanon contends that a portion of the Leviathan natural gas field, off Israel's coast, lies within its maritime borders.
Scarlett Johansson steps out with fiance after pregnancy reveal
Senate Democrats to pull all-nighter on climate change