Potters boss Mark Hughes has been heavily linked with a move for Redmond as he looks to draft in at least one new winger, but he has yet to strike a deal with the Canaries.
Norwich are believed to be holding out for a fee in the region of £6million, but Stoke are only willing to pay half of that. Now reports claim that Saints have entered the running and they could be willing to match the valuation as they desperately try to bring in some much-needed reinforcements following a mass exodus.
Saints boss Ronald Koeman knows he will need to spend plenty of the money the club have recouped so far to placate fans before the new season begins and has targeted Canaries winger Redmond, who impressed in the Premier League last season following a £2million move from Birmingham.
He is keen to stay in the top flight after Norwich's relegation to the Championship and move to either Stoke, Southampton or Newcastle would appeal.