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Recent detections of extended Lyman-α halos around Lyα emitters (LAEs) have been reported on a regular basis, but their origin is still under investigation. Simulation studies predict that the outer regions of the extended halos contain a major contribution from the Lyα emission of faint, individually undetected LAEs. To address this matter from an observational angle, we used halo occupation distribution (HOD) modeling to reproduce the clustering of a spectroscopic sample of 1265 LAEs at 3 < z < 5 from the MUSE-Wide survey. We integrated the Lyα luminosity function to estimate the background surface brightness due to discrete faint LAEs. We then extended the HOD statistics inwards towards small separations and computed the factor by which the measured Lyα surface brightness is enhanced by undetected close physical neighbors. We considered various clustering scenarios for the undetected sources and compared the corresponding radial profiles. This enhancement factor from LAE clustering depends strongly on the spectral bandwidth Δv over which the Lyα emission is integrated and this value can amount to ≈20 − 40 for small values of Δv (around 200 − 400 km s−1) as achieved by recent studies utilizing integral-field spectrographic data. The resulting inferred Lyα surface brightness of faint LAEs ranges between (0.4 − 2)×1020 erg s−1 cm−2 arcsec−2, with a very slow radial decline outwards. Our results suggest that the outer regions of observed Lyα halos (R ≳ 50 pkpc) could indeed contain a strong component from external (but physically associated) LAEs, and may even be dominated by them. It is only for a relatively shallow faint-end slope of the Lyα luminosity function that this contribution from clustered LAEs would be rendered insignificant. We also confirm that the observed emission from the inner regions (R ≤ 20 − 30 pkpc) is too bright to be substantially affected by clustering. We compare our findings with predicted profiles from simulations and find good overall agreement. We outline possible future measurements to further constrain the impact of discrete undetected LAEs on observed extended Lyα halos. [ABSTRACT FROM AUTHOR]