Jorgensen joined Vale last month on a non contract basis after he was released by Blackpool at the end of last season.
And after making five sub appearances for Micky Adams’ side, it looked like he would become a permanent fixture at the club.
But Vale cannot match his wage demands so the player has moved on to seek employment elsewhere.
The Vale boss told the club's official website: "We put an offer on the table, which unfortunately Claus has decided to turn down.
"We are obviously disappointed, but he is now considering other options and there is nothing we can do about that except wish him luck."