The 25-year-old has only recently returned from a long-term thigh injury which kept him sidelined for more than a year, but he is behind the likes of Dele Alli, Christian Eriksen and Son Heung-min in the Spurs pecking order as things stand.
Tottenham are also expected to complete the signing of Lucas Moura from Paris Saint-Germain before the 11pm transfer deadline this evening, which would see Lamela's first-team chances become even more limited.
The Argentine has 18 months remaining on his current deal, but The Independent reports that Spurs would only be willing to allow him to leave on loan.
Southampton could face competition for his signature from former club Roma, though, with the Serie A side understood to also be interested.
Lamela has made just three starts for Spurs across all competitions this season.