We suggest and study the formation of intermediate luminosity optical transients (ILOTs) from the merger of two cool giant stars. For the two stars to merge when both are in their giant phases, they must have close masses at their zero-age main sequence, and the orbital separation must be in the right range. After the two giants merge, the two cores spiral in toward each other within a common envelope. We study the energy sources of radiation in this process, which includes the ejection of mass that powers radiation by both recombination and by collision with previously ejected mass. This process includes no jets, unlike many other types of ILOTs, hence the event will not form a bipolar nebula. Using the stellar evolution numerical code mesa for two binary systems with stellar masses of (15M o˙, 15.75M o˙) and (31M o˙, 31.5M o˙), we find that the merger of the two cores releases gravitational energy that marginally ejects the entire common envelope. This implies that in many cases the two cores merge, i.e., a fatal common envelope evolution, leading to a somewhat more luminous ILOT. A typical ILOT from the merger of two cool giant stars lasts for several months to several years, and has a typical average luminosity of, where M CE is the ejected common envelope mass. The merger-driven massive outflow forms dust, hence leading to a very red ILOT, possibly even infrared luminous and undetectable in the visible.