  FU Ori-type stars are young stellar objects (YSOs) experiencing luminosity
outbursts by a few orders of magnitude, which last for $\sim$$10^2$ years. A
dozen of FUors are known up to date, but many more currently quiescent YSOs
could have experienced such outbursts in the last $\sim$$10^3$ years. To find
observational signatures of possible past outbursts, we utilise 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 N$_{2}$H$^{+}$ $J=3-2$, C$^{18}$O $J = 2-1$,
H$_2$CO $(J_{\rm K_a, K_c}) = 4_{04}-3_{03}$, 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, N$_2$H$^+$ and H$_2$CO line fluxes
from the literature, we identify ten nearby disc systems that might have
undergone FU Ori outbursts in the past $\sim$$10^3$ years: [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.

Solar and Stellar Astrophysics;Earth and Planetary Astrophysics;Astrophysics of Galaxies