Charm and beauty quark production measurement represents a fundamental means to access the initial stage of hadronic collisions. Being produced almost exclusively in initial hard partonic scatterings due to their large masses, $m_{\text{c}}=$ 1.3 $ \text{GeV}/c^2$ and $m_{\text{b}} =$ 4.1 $ \text{GeV}/c^2$, charm and beauty quarks are ideal tools to investigate various QCD aspects.
In addition, the corresponding measurements in pp collisions represent a baseline for cold nuclear matter studies in p--A collisions as well as for the characterization of the hot and dense interacting nuclear matter, the quark--gluon plasma (QGP), formed in A--A interactions.

An analysis technique that was little investigated until now at LHC energies to measure $\text{c}\overline{\text{c}}$ and $\text{b}\overline{\text{b}}$ cross sections consists in exploring the high-mass regions of the dilepton invariant mass spectrum, more precisely the two continuum regions between charmonium and bottomonium resonances $\text{(4} < m_{\mu^{+}\mu^{-}} <\text{ 9 GeV}/c^2$) and above the bottomonium states ($m_{\mu^{+}\mu^{-}}> $ 11 $ \text{GeV}/c^2$). Indeed, these regions are significantly populated by the semileptonic decays of hadron pairs containing charm and beauty quarks.

In these proceedings, the status of this study is shown, discussing the details of the analysis procedure foreseen to measure the charm and beauty cross sections. In particular, the results of PYTHIA8 simulations for pp collisions at $\sqrt{s}$ = 13 TeV in the rapidity region 2.5 < \textit{y} < 4 covered by the ALICE muon spectrometer, crucial to address the different components to the dimuon yield, are presented.