But the Dutch side could miss out as Gamba Osaka are interested in taking him back to Japan.
What seems certain is that Inamoto will leave Arsenal after a frustrating time in the Premiership.
But there is confusion over the conditions of his transfer to the London club, with suggestions that his move was never made permanent.
There has been no confirmation from either club, but it seems likely that Inamoto only joined Arsenal on loan with a view to a permanent move.
If that is the case, his registration would automatically revert back to Gamba Osaka.
But Inamoto has suggested that he is keen to continue his career in Europe and Feyenoord are at the front of the queue of clubs wanting to sign him.
"We have been monitoring Inamoto's situation at Arsenal," Feyenoord general manager Rob Baan told his club's official website.
"We have been interested in Inamoto since (Shinji) Ono signed for us."
But first Gamba Osaka will try to persuade the midfielder to return to Japan.
"We will have talks about his future and they will include the possibility of his return to Gamba Osaka," said a club statement issued by the J-League outfit.
The statement added that Wenger, who is in Japan working as a commentator at the World Cup, had met with the player and agreed that he could leave.
Inamoto became the first Japanese player to join an English club last summer but he only featured in four matches for Arsenal last season - two in the Champions League and two in the English League Cup.
The 22-year-old has made a much bigger impact at international level, scoring two goals against Belgium and Russia to help Japan reach the second round of the World Cup.