The Merseyside club sacked Kenny Dalglish last week following a disappointing eighth-placed Premier League finish. And the Dutchman, who is believed to be on the Reds' radar after leading the Amsterdam side to two consecutive Eredivisie titles, insists he is not thinking about moving on yet,
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"In Amsterdam we are on a new path along with the club and Wim Jonk and Dennis Bergkamp, my colleagues on the backroom staff.
"That's why I will stay loyal to Ajax in the years to come."
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.