The out of favour Saints striker is reportedly wanted by his former boss at Everton, and former club QPR.
Toffees boss Ronald Koeman brought Austin to St. Mary's in January, but the 27-year-old has made just two starts in that time and began the Claude Puel era on the bench.
However, Austin remains highly rated by Koeman, according to the report, and the Dutchman is said to be eyeing him as one of two offensive additions which could potentially pave the way for Romelu Lukaku's departure to Chelsea.
Before his £4 million switch to the South Coast, Austin enjoyed a prolific spell at QPR, where he scored 47 goals in 89 appearances.
And the report adds that the R's are considering trying to convince the one-time England call-up to return to Loftus Road on loan, following a promising start to the new campaign which has seen them top the Championship with maximum points from two matches.
However, Austin wants to remain in the Premier League, according to the report, which adds that a reunion with Koeman is likely to appeal.
Koeman left Southampton for Everton in July
It is claimed that Chelsea's Loic Remy could also end up at Goodison Park, with the Blues reportedly considering adding him to their offer for former player Lukaku (below), who Everton value at £75 million.