  The observed muon anomalous magnetic moment deviates from the Standard Model
predictions. There are two scalar leptoquarks with simultaneous couplings to
the quark-muon pairs of both chiralities that can singly explain this
discrepancy. We discuss an alternative mechanism that calls for the mixing of
two scalar leptoquarks of the same electric charge through the interaction with
the Higgs field, where the two leptoquarks separately couple to the quark-muon
pairs of opposite chirality structures. Three scenarios that satisfy this
requirement are $S_1\,\&\, {S}_3$, $\widetilde{S}_1\,\&\, S_3$, and
$\widetilde{R}_2\,\&\, R_2$, where the first scenario is realised with the
up-type quarks running in the loops while the other two scenarios proceed
through the down-type quark loops. We introduce only two non-zero Yukawa
couplings to the relevant quarks and a muon, at the time, to study ability of
these three scenarios to explain $(g-2)_\mu$ and be in accord with available
experimental constraints. We find that the $S_1\,\&\, {S}_3$ scenario with the
top-quark loops is consistent with all existing measurements. The
$\widetilde{S}_1\,\&\, S_3$ and $\widetilde{R}_2\,\&\, R_2$ scenarios can
accommodate the observed discrepancy through the bottom-quark loops but exhibit
significant tension with the existing data on the high-$p_T$ dilepton-tails at
LHC for the required values of Yukawa couplings and leptoquark masses.
