Olivier Giroud has come in for some criticism this season for labored performances after a strong start to the campaign.
However, the France international could well have been playing his football in Holland had things worked out differently.
The former Netherlands defender went on to admit that the club are always in the market for future stars and had a look at Xherdan Shaqiri when he was at Basel.
"We're still looking for these boys. But you also have to have a bit of luck,” De Boer told FOX Sports.
"(Board member) Tonny Bruins pointed us towards Olivier Giroud when he played for Montpellier. He had also been quick to notice Xherdan Shaqiri.
"But if those guys happen to score often for a few weeks, then you get Arsenal and Bayern Munich at the doorstep. Then you have no chance."
Giroud’s position at Arsenal is still unclear, with persistent rumours that Arsene Wenger will look to add a new centre forward to his squad this summer.