Vale had accepted a bid from the Tykes for Constantine but the player has failed to agree terms and the deal is now off.
"Leon's deal fell through late this afternoon at their end, so he will be back in training on Wednesday morning with the kids," manager Martin Foyle told the club's official website.
"He will be involved in Saturday's game against Northampton in some capacity, depending on his frame of mind.
"I will sit down and have a talk with him and assess the situation."