The 22-year-old signed with Spurs when he was only 15 years old, but only managed to make four first-team appearances during his time at the club.
The Republic of Ireland international spent time on loan at Millwall, Ipswich Town, MK Dons, Preston and Dutch side Excelsior, where he scored 17 goals in 32 games last season.
Spurs opted to sell Parrott in the summer, with the forward joining AZ Alkmaar in a €8 million (£6.7m) deal.
Parrott has made an impressive start at AZ with six goals in nine matches so far, four of which came in the 9-1 win against SC Heerenveen last month.
But speaking on Ziggo Sport, former Chelsea defender, Khalid Boulahrouz, raised doubt over the striker’s potential.
‘Parrott has scored six [this season] but I don’t think he is a deadly striker yet. He’s not someone where I think, ‘you are now taking AZ to a higher level’,’ said Boulahrouz.
Van der Vaart, however, disagreed with Boulahrouz’s analysis of the former Tottenham forward.
‘I think so, I think he’s going to be a very big player,’ Van de Vaart replied.
‘I don’t know what it is. I saw him at Excelsior, but then it was more on the counter.
‘Now he is a good, footballing striker, who actually has everything. He just has to develop the killing a bit.
‘He can perhaps play football a little too well to be a killer.
‘Then you start wandering a bit and that costs strength. In the final phase you lack some strength to score. I really think he is a gem.’
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