FU Ori-type stars (FUors) are young stellar objects (YSOs) experiencing luminosity outbursts by a few orders of magnitude, which last for ∼102 yr. A dozen of FUors are known up to date, but many more currently quiescent YSOs could have experienced such outbursts in the last ∼103 yr. To find observational signatures of possible past outbursts, we utilize ANDES, RADMC-3D code as well as CASA ALMA simulator to model the impact of the outburst on the physical and chemical structure of typical FU Ori systems and how it translates to the molecular lines’ fluxes. We identify several combinations of molecular lines that may trace past FU Ori objects both with and without envelopes. The most promising outburst tracers from an observational perspective are the molecular flux combinations of the N2H+J = 3–2, C18O J = 2–1, H2CO ⁠, and HCN J = 3–2 lines. We analyse the processes leading to molecular flux changes and show that they are linked with either thermal desorption or enhanced chemical reactions in the molecular layer. Using observed CO, HCN, N2H+, and H2CO line fluxes from the literature, we identify ten nearby disc systems that might have undergone FU Ori outbursts in the past ∼103 yr: [MGM2012] 556, [MGM2012] 371, and [MGM2012] 907 YSOs in L1641, Class II protoplanetary discs around CI Tau, AS 209, and IM Lup and transitional discs DM Tau, GM Aur, LkCa 15, and J1640-2130.