Abstract We study the $$J/\psi \rightarrow K^+ K^- f_0(980)(a_0(980))$$ J/ψ→K+K-f0(980)(a0(980)) reaction and find that the mechanism to produce this decay develops a triangle singularity around $$M_{\mathrm{inv}}(K^- f_0/K^- a_0) \approx 1515$$ Minv(K-f0/K-a0)≈1515 MeV. The differential width $$d\varGamma / dM_{\mathrm{inv}}(K^- f_0/K^- a_0)$$ dΓ/dMinv(K-f0/K-a0) shows a rapid growth around the invariant mass being 1515 MeV as a consequence of the triangle singularity of this mechanism, which is directly tied to the nature of the $$f_0(980)$$ f0(980) and $$a_0(980)$$ a0(980) as dynamically generated resonances from the interaction of pseudoscalar mesons. The branching ratios obtained for the $$J/\psi \rightarrow K^+ K^- f_0(980)(a_0(980))$$ J/ψ→K+K-f0(980)(a0(980)) decays are of the order of $$10^{-5}$$ 10-5 , accessible in present facilities, and we argue that their observation should provide relevant information concerning the nature of the low-lying scalar mesons.