Speedy and on-time detection of coronavirus disease 2019 (COVID-19) is of high importance to control the pandemic effectively and stop its disastrous consequences. A widely available, reliable, label-free, and rapid test that can recognize tiny amounts of specific biomarkers might be the solution. Nanobiosensors are one of the most attractive candidates for this purpose. Integration of graphene with biosensing devices shifts the performance of these systems to an incomparable level. Between the various arrangements using this wonder material, field-effect transistors (FETs) display a precise detection even in complex samples. The emergence of pioneering biosensors for detecting a wide range of diseases especially COVID-19 created the incentive to prepare a review of the recent graphene-FET biosensing platforms. However, the graphene fabrication and transfer to the surface of the device is an imperative factor for researchers to take into account. Therefore, we also reviewed the common methods of manufacturing graphene for biosensing applications and discuss their advantages and disadvantages. One of the most recent synthesizing techniques - laser-induced graphene (LIG) - is attracting attention owing to its extraordinary benefits which are thoroughly explained in this article. Finally, a conclusion highlighting the current challenges is presented.