The 24-year-old right-back's contract expires at the end of next season, and Feyenoord have now given up trying to convince Janmaat to sign a new deal.
He is thought to be on Arsene Wenger's shortlist of possible replacements for Arsenal's current first-choice right-back, Bacary Sagna.
The French international looks likely to leave the Emirates Stadium at the end of the season as he is yet to agree an extension.
Feyenoord technical director Martin van Geel is awaiting interest from overseas clubs in Janmaat and his defensive partner Stefan de Vrij.
Both Janmaat and de Vrij are in similar situations regarding their contracts, and the club is now open to offers for the pair this summer.
Van Geel said: "Those conversations [over new contracts] are shut down. We await the summer."
Both are expected to play at the World Cup with the Netherlands this summer, which Feyenoord hope will increase their value. The Dutch club want to pay off their debts, and believe they can clear a significant portion through player sales.
If Arsenal, or any other club, does not follow up with a bid over the summer Feyenoord may revisit contract negotiations.
But for the time being, it looks like they're preparing for their exits at the end of the season.