Southampton manager Mauricio Pellegrino is reportedly very keen on bringing the Dutchman to St. Mary's before the transfer deadline on Wednesday.
However, the Premier League club are going to need to splash the cash after their first bid of £25m was allegedly rejected by Spartak, who want at least £30m.
It would mean that Pellegrino would have to break the club's transfer record for the second time this January after buying Guido Carrillo from Monaco for £19.1m on Thursday.
Promes appears to be well worth the money after scoring 53 goals in 101 Russian Premier League appearances since joining from FC Twente in August 2014 for a reported £12m.
Not only that but the 26-year-old was crowed Russian Premier League footballer of the year in 2017 and has been capped 25 times for the Netherlands.