Former Birmingham defender Bruce, son of current Wigan boss Steve, who was a team-mate of Keane's at Manchester United, was offered a deal earlier in the season by previous manager Jim Magilton, but turned down the contract as the terms were deemed unacceptable.
Speaking to the Official Club Website, Bruce said: "It's a big couple of weeks for the players who are out of contract in particular.
"It's a fresh start for us and we have two weeks to show the manager that we are worth a new deal. We are going to have to train hard and deliver on the pitch and see where it leads. It's going to be a case of sink or swim.
"It's been well documented that I was offered a new contract but I felt that it wasn't what I was looking for.
"It's a chance for myself to show the new manager that I'm worth keeping around and we will see what happens over the next two weeks."
Click here for a profile of Alex Bruce or Click here for a game by game rundown of his season to date.