The outstanding shot stopper impressed in the Eredivisie last season and is being linked to Liverpool.
He is seen as an option if Caoimhin Kelleher, the club's no.2 keeper, decides to leave this summer.
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Those are two very nice clubs," said Bijlow about the Reds and Arsenal.
"Of course it is always nice to be mentioned at big clubs. What I'm just saying is: I'm ambitious.
"As long as I play for Feyenoord, I'll give everything for that and first I just want to focus on the Dutch team.
Would I stay at Feyenoord? You never know, do you? That's football. You don't know that. I'm ambitious, I've always said that. If the opportunity presents itself and a good club comes from abroad, I am open to it. I've always said that. As long as I am under contract with Feyenoord, that is never a punishment and I will give everything as long as I play there."