The 42-year-old has led the Amsterdam side to two consecutive Eredivisie titles since joining in 2010 and has no intention to replace Kenny Dalglish at Anfield
The Merseyside club sacked Kenny Dalglish last week following a disappointing eighth-placed Premier League finish, and they had earmarked the Dutchman as a possible replacement.
However, De Boer, who led the Amsterdam side to two consecutive Eredivisie titles, insists he is not thinking about moving on yet.
"I feel honoured by their approach, but I only just started at Ajax," he told De Telegraaf.
"We just started a new project here in Amsterdam together with Wim Jonk and Dennis Bergkamp, my colleagues at the club's technical heart, and that's why I will remain loyal to Ajax for the next few years."
The 42-year-old has been in charge at the Dutch club since December 2010, when he initially took the role on an interim basis following now-Fulham boss Martin Jol's resignation.
He spent time as Netherlands' assistant boss at the 2010 World Cup and enjoyed a distinguished playing career in which he won five Eredivisie titles and one Champions League.