Given feels that making the decision earlier will give the new manager the opportunity to learn from seeing his players in competitive action, as opposed to seeing them in friendlies used in the build-up to qualification for Euro 2016.
"I think the sooner it is done the better and make a decision as quick as possible," Given told RTE.
"Get the new manager for these games next month and he can look players that are there already, freshen things up and bring some of his own ideas and new players in.
"It is all well and good doing that in friendlies but I think it is even better if a new manager can do it in competitive games. I think it is important we don't finish with a whimper, that we get good results and try and finish as high as we can."