By Wayne Veysey | Chief Correspondent
But it is understood that they face competition from Arsenal, whose scouts have been regular visitors at the Amsterdam Arena this season to run the rule over the Ajax goalkeeper.
Arsene Wenger is a big admirer of the 28-year-old and is still pursuing an established goalkeeper despite the startling assurance displayed by 20-year-old Wojciech Szczesny since replacing the injured Lukasz Fabianski two months ago.
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Stekelenburg’s contract expires in 2012 and Ajax accept that the next transfer window will be the time to cash in on a player who joined them at 15 and whom they value at between €10 million (£8.4m) and €12m (£10.1m).
Arsenal have also been closely monitoring Stekelenburg’s club colleague Vertonghen, who has told Ajax that he wants to move to the Premier League this summer.
The Belgium international is a close friend of his countryman and fellow centre-back Thomas Vermaelen and Arsenal would be his first choice of club, although he is also being closely monitored by AC Milan.
Arsenal-bound? | Stekelenburg has emerged as a top target for Arsene Wenger
Ajax have put a relatively modest €8m (£6.7m) price tag on Vertonghen, although a bidding war would be likely to increase his fee.
Arsenal’s concerted interest in Stekelenburg is unlikely to deter Manchester United from moving in on the 6ft 6in shot-stopper. Rene Meulensteen, first-team coach at Old Trafford, told Dutch radio last month that “Stekelenburg is indeed a keeper who is at the top of our wanted list”.
A source told Goal.com UK: “The problem with Ajax is that they have a very good team but he [Stekelenburg] has only one season left on his contract in the summer. Manchester United are keen and Arsene is also a big fan.
“Arsenal have been watching Vertonghen for a long time and he wants to join Vermaelen. He fits the bill for Arsenal because he is calm, comfortable in possession and has a strong mentality.”
Any movement by Arsenal for another senior goalkeeper would signal the end of Manuel Almunia’s career at Emirates Stadium.
The Spaniard, who is deputising Szczesny after returning from a long-term elbow injury, has been told that he will not be offered a new contract when his current deal ends in 2012.