Kevin Blackwell is in charge of the team for this weekend's final game of the season at Chelsea.
A permanent appointment will depend on a wide range of issues due to come to a head over the coming weeks with takeover talks still on-going with potential new owner Steve Parkin.
Iain Dowie is thought to be the favoured choice of Parkin should he take control.
"There will be a board meeting to discuss the possible candidates to replace Eddie," confirmed Lorimer in the Yorkshire Post. "We will be putting some names forward and see who we think are the right men for the job. It has to be someone who wants the job, has a passion for the challenge ahead of them and appreciates what a big club Leeds is. It's important we get the right person but there is not a lot of time available because the players are back in training in eight weeks' time so the new manager will need to work with them and prepare for the new season.
"Several names have been mentioned, including Gordon Strachan and he is someone we will be talking about. He has the qualities required and had proved himself a highly-capable good manager. Iain Dowie has also been mentioned and he is also doing well, although he is obviously in a job."
Gray will not be involved with the team selection this weekend while his new role 'advising the board on footballing issues' starts June 1.