The Argentine has been linked with several Premier League clubs, including Arsenal, Tottenham Hotspur, West Ham United and Newcastle United, but could be interested in linking up with his compatriot, Pochettino, at St Mary's.
Biglia has been on strike in his attempts to force a move to England during the January transfer window and it remains to be seen what his future holds.
But he was expected to return to Anderlecht this week when discussions are likely to take place.
Anderlecht boss Herman van Holsbeeck said on Sunday: "Biglia will start back next week."
Pochettino, who succeeded Nigel Adkins on Friday after the ex-Southampton boss' shock sacking, has also been linked with midfielder Joan Verdu.
The Spaniard has just six months left on his contract at Pochettino's former club, Espanyol.