Wiss on his way out
The Finnish midfielder is currently in negotiations with his hometown team, Tampere about a move in the January transfer window.
The Hibs boss has several injury concerns for the game against Aberdeen at the weekend but will not consider the 31-year-old for the match.
"We knew over the course of a long season that we'd pick up injuries and suspensions and that we are running a tight ship," stated Williamson to the Edinburgh Evening News.
"It's incredible that all the players out are left-sided but that's the way it is.
"Jarkko could be away in a few weeks' time but I'm looking ahead and we won't be taking a backward step by introducing him back into the team."
He added: "I'm more concerned with the long-term future of the club and this could provide another opportunity for someone to stake a claim for a place in the side."