Offshore wind energy production is non-existent in Brazil, although is currently considered in the country's expansion plans. New and promising oil and gas fields have recently been discovered in the Sergipe and Alagoas basin, corresponding to one third of current Brazilian production. This work analyzes the technical and economic viability of an Offshore Wind Farm to supply the energy demand of a Floating Liquified Natural Gas proposed to be used in those fields. The resulting estimated cost of capital and levelized cost of energy were in line with international values. However, the project proved to be unfeasible due to the high cost for its size and the low average price of energy generation. Nonetheless, the synergy between the oil and gas sector and offshore wind may include benefits such as the reduction of greenhouse gas emissions within the sector itself, making the non-renewable resource available for more noble use.