For the time being, Ajax are only in light contacts with Gomes’ camp and have not made any offers.
Gomes is under contract with Sao Paulo until March 2023 and is a Brazil under-23 international.
In the most recent Brazilian Série A season, the central midfielder appeared 27 times, scoring twice and assisting two goals.
Ajax have signed two big talents from Sao Paulo in recent years and the clubs enjoy a good relationship.
The Eredivisie champions paid €12m for David Neres in 2017 and he has proven to be a good signing.
And earlier this year, Ajax struck a deal with Sao Paulo for another Brazil under-23 starlet, Antony.
Antony is hoping to move to Europe in July and Gomes could follow if the interest materialises.
To make a potential move to Europe easier, Gomes is in the process of getting a Portuguese passport.
That will ensure that he would not take a non-European squad place if he joins Ajax or another side.