The Dutch team are hoping that the goalkeeper will reject any approaches from the Reds, and other English teams, to continue his development in Amsterdam
The Reds have been closely following the progress of the Dutch talent, who, at 15, would only be eligible to sign a professional contract next year.
Ajax are hopeful the teenager will ignore any approach from the Merseysiders - one of several English sides monitoring the goalkeeper- to continue his development in Amsterdam.
Ruijgrok is one of several youngsters under consideration by Liverpool, who are determined to develop their academy into one of the best in the world.
The Reds saw an academy star hit the headlines on Tuesday night as 17-year-old midfielder Ben Woodburn became the club's youngest ever scorer by finding the net against Leeds.
Having been handed his debut by Jugen Klopp in the Premier League win over Sunderland, Woodburn smashed home in front of the Kop to beat Michael Owen's record by 98 days.