The Danish wide man was the subject of an approach from the Bundesliga outfit but PSV dismissed it out of hand, claiming the offer was far below their valuation of the player.
However, Arnesen has revealed that PSV have encouraged Hamburg to come back with a better offer, suggesting Rommedahl's future may be away from Eindhoven.
"It's correct that Hamburger SV have showed interest in Rommedahl," Arnesen told Ritzau.
"They have offered ‚é¼1.5 million and that is not enough.
"We have asked them to return with a better offer, but have not heard anything yet.
"However, at times, it can happen quickly."
