Reports emerged on Tuesday claiming that the Premier League club's latest £25m bid for the Dutch international had still been rejected by Spartak with the deal collapsing on transfer deadline day.
However, Mauricio Pellegrino wants to make another move for Promes in summer when the Russian side may be more willing to part the winger.
'Saints' reportedly believe that this is the best strategy after being convinced that the 26-year-old wants to come to St. Mary's in what would likely be a club-record fee.
Promes has scored 10 goals in 17 Russian Premier League games this season, as well as two in the Champions League, and would have been a perfect addition to Pellegrino's squad as they've lacked a cutting edge in front of goal this campaign.
Southampton are going to have to rely on other sources as they find themselves in a closely-contested Premier League relegation battle with the bottom eleven teams separated by eight points.