This is according to The Daily Mail, who suggest that Ajax chief De Boer will hold talks over succeeding Tim Sherwood - who appears set to depart this summer - and that he would be keen to continue his partnership with Bergkamp, his assistant who has played a major role in the success enjoyed by the Eredivisie giants in recent years.
The same source further suggests that De Boer is understanding of the delicate situation Bergkamp could be placed in as a result, with his compatriot having secured iconic status among the Arsenal faithful thanks to a successful 11-year stint with the club between 1995-2006.
While Tottenham have today moved swiftly to deny suggestions that they have approached Ajax or indeed any other club regarding their coaching staff, it is still nevertheless interesting to ponder the possibility of Bergkamp potentially moving to White Hart Lane and what impact such a switch would have on his popularity across the North London divide.
As a player with Arsenal, Bergkamp epitomised Arsene Wenger's commendable approach to the game with his excellent ability, grace, poise and skill.
Widely admired for such qualities and his unwavering eye for goal, Bergkamp's time with Arsenal was hugely successful, with the club even dedicating a statue to a man who won four Premier League titles and three FA Cups with the Gunners.
Arsenal fans - what do you make of such rumours that Bergkamp could move to Tottenham and how do you think it would impact upon his lofty standing at the Emirates?
Do you think Bergkamp would follow De Boer to White Hart Lane? Let us know your thoughts below.
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