De Boer, who has guided the Amsterdam giants to back-to-back Eredivisie titles, revealed the approach by the Reds to a Dutch newspaper.
Some bookmakers had the 42-year-old as second-favourite for the job, behind ex-Chelsea boss Andre Villas-Boas, but the former defender wants to continue his project at the club where he spent the majority of his playing career.
"I am honoured by the request, but I am only just getting started with Ajax," De Boer told De Telegraaf.
"In Amsterdam we are on a new path and, along with the club and Wim Jonk and Dennis Bergkamp, my colleagues in the technical heart, I want to bring good things. That's why I will stay loyal to Ajax in the coming years."
De Boer is the second manager to turn down Liverpool's advances as owners Fenway Sports Group look for candidates to replace Kenny Dalglish, who was sacked last week. Swansea City boss Brendan Rodgers rejected an approach last week.
Villas-Boas and Wigan manager Roberto Martinez are now seen as the front-runners for the position.