The 22-year-old centre back enjoyed a break-out season at Rangers during the 2021/22 campaign, playing a prominent part in their run to the Europa League final.
Sky Sports are now reporting that both the Dutch champions and the Premier League side are interested in signing the versatile defender, who can operate at centre or left back.
Bassey has previously been linked with a move to Aston Villa, where he would join former Gers manager Steven Gerrard.
However, Sky Sports is now reporting that seven sides are chasing the Rangers defender, including teams in Serie A and the Bundesliga.
Ajax have a bit of cash in the bank, after agreeing to sell defender Lisandro Martinez to Manchester United.
Should Bassey be allowed to leave Ibrox - just years after he arrived from Leicester City for around £230,000 - he could break Rangers’ record transfer fee for the second season in a row.
It is understood that the Govan giants could ask for at least £20 million for the Nigerian.