The Netherlands international continues to be linked with the Bundesliga side, whose coach is keen to be reunited with the 29-year-old, who previously played under him at Hamburg
The Spurs attacker's representative, Robert Geerlings, recently revealed interest from the Bundesliga side in the German press, while the club chairman Clemens Tonnies also suggested a move for the Dutch international could be on the cards, though it would be a "complicated" transfer.
And now, Stevens, who coached Van der Vaart while in charge of Hamburg in 2007-08, has indicated he would like to be reunited with the 29-year-old.
"His qualities are tremendous," Stevens told Voetbal International.
"Schalke won't say no to Van der Vaart, I still know him from our mutual stay at Hamburger SV and would like to join forces with him again. We are in contact with his agent. I'm on holiday right now, but I'm in toch with Schalke GM Horst Heldt on a daily basis about our plans.
"I don't know how Raf himself feels about a return to Germany. I haven't spoken him yet, he's with his mind on the Euros. His agreement with Tottenham is still running, so it seems that we have to pay a transfer sum in case he would come.
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"Let's be clear: if Raf really wants to come, he's more than welcome. If we have this opportunity to contract him, which looks quite reasonable, we won't miss our chance. The attacking midfielder-position, it is possible to shuffle within our squad. Julian Draxler, for example, is only eighteen years old, while Van der Vaart is a very experienced player."
Publicly though, Van der Vaart, who featured as the Netherlands suffered a shock defeat in their Euro 2012 opener against Denmark, has stated he is happy to remain at Tottenham.
"There is always an interest [from other clubs]. But I am happy in England and I want to stay," he told Sky Sports News four days ago.
"I only said that in soccer everything is possible - but not at anytime."