It has been reported by The Sun that the Gunners are planning a 25 million pound move for the 28-year-old Dutch forward.
The report in the British tabloid has added that the Netherlands international would make the switch to the North London outfit.
It has been further claimed that Ajax head coach Erik ten Hag would be willing to sell the forward.
Ajax spell
Promes joined Dutch giants Ajax from Spanish club Sevilla in the summer of 2019 for 14 million pounds.
The Netherlands international forward made 18 starts and two substitute appearances in the Eredisvie this past season, scoring 12 goals and providing four assists in the process.
The 28-year-old also scored four goals in five Champions League matches and played 45 minutes in the Europa League for Ajax in 2019-20.
Arsenal finished eighth in the Premier League table in 2019-20 and will play in the Europa League next season after winning the FA Cup.