The 28-year-old joined the Dutch champions from Sevilla last June and has been in impressive form during the 2019-20 campaign, scoring 15 times in 24 appearances in all competitions.
According to Russian website Sport.ru, both Liverpool and Chelsea are currently tracking the Netherlands international ahead of a potential move at the end of the season.
The report, though, claims that Ajax value the versatile attacker in the region of €40m (£34.6m) and would not be prepared to sell him for less.
Promes, who has been capped on 40 occasions by the Dutch national team, left Sevilla after one season last summer having struggled to settle at the Estadio Ramon.
The winger's contract in Amsterdam will run until the end of the 2023-24 campaign.