The Portugal international, 27, has been allowed to leave St Mary’s as part of Ralph Hasenhuttl’s shake-up this month.
Hasenhuttl has given Soares just one start in the Premier League since taking over from Mark Hughes and getting the club out of the relegation zone.
The clubs are in talks over a permanent deal, with Inter targeting a right-back and tracking Ashley Young and Antonio Valencia from Manchester United.
But Soares is now in pole position with sources close to the ex-Sporting Lisbon star hopeful that a deal can be thrashed out.
Soares has just one full season left on his deal at Saints.
However, they could look to cash in now after Hasenhuttl made him available.
The Austrian coach wants to work with a smaller squad for the second half of the season.
The St Mary's chief has already allowed Manolo Gabbiadini to leave for Sampdoria.
Meanwhile, Wesley Hoedt has been shipped out on loan to Celta Vigo until the end of the season.
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