The 31-year-old is expected to leave the south coast club this summer following their relegation from the Premier League last season.
He is not keen on playing in the Championship and is waiting for concrete offers to land on his table.
Armstrong has suitors in the Premier League but he would prefer a move to Europe in the ongoing transfer window.
And according to local Turin daily Tuttosport (via Tutto Mercato), Torino have been offered a chance to sign the player this summer.
Armstrong’s agents have been sounding out clubs in Europe and Torino have been contacted for a potential switch.
The Serie A side are in the market for players and are weighing up a move for Armstrong ahead of the new season.
They are likely to have competition in Italy for his signature as Lazio are interested in signing him.
He is in the final year of his contract and is likely to be available for a cut-price fee this summer.