Authors’ abstract: The Gruenberg-Kegel graph (or the prime graph) \( \Gamma (G)\) of a finite group \(G\) is the graph whose vertex set is the set of prime divisors of \( |G|\) and in which two distinct vertices \(r\) and \(s\) are adjacent if and only if there exists an element of order \(rs\) in \(G\). A finite group \(G\) is called almost recognizable (by Gruenberg-Kegel graph) if there is only a finite number of pairwise non-isomorphic finite groups having Gruenberg-Kegel graph as \(G\). If G is not almost recognizable, then it is called unrecognizable (by Gruenberg-Kegel graph). Recently P. J. Cameron and the first author [J. Algebra 607, 186–213 (2022; Zbl 1516.20050)] have proved that if a finite group is almost recognizable, then the group is almost simple. Thus, the question of which almost simple groups (in particular, finite simple groups) are almost recognizable is of prime interest. We prove the following nice result: every finite simple exceptional group of Lie type, which is isomorphic to neither \(^2B_2(2^{2n+1})\) with \(n\geq 1\) nor \(G_2(3)\) and whose Gruenberg-Kegel graph has at least three connected components, is almost recognizable. Moreover, groups \(^2B_2(2^{2n+1})\) with \(n\geq 1\) and \(G_2(3)\) are unrecognizable.