Corbin led the search process, Lindsey said, and drew from a list of personally selected names.
"We're getting close but we're not going to announce anything prematurely," said Lindsey, who is with Corbin on a trip.
Austin Toros coach Brad Jones has been mentioned several times as a favored candidate. The Toros are San Antonio's Development League affiliate, and Jones a nephew of former Jazz coach Jerry Sloan has ties with Corbin.
Asked about Jones being added to Utah's staff, Lindsey declined comment.
"I don't have anything to tell you … other than we do have a concrete direction and we're hopeful that one thing in particular will come through," said Lindsey, replying to a general question about the hire. "We think we're close, but we've got to button up a lot of details."
Meanwhile, the Jazz officially confirmed Layden's previously reported departure on Wednesday via a statement.
Speaking with The Tribune, a humble Layden thanked the Jazz for a 25-year relationship that covered several eras in the organization's history. He had three runs with Corbin, a decade-plus association with former assistant Phil Johnson and Sloan, and enjoyed a highly successful tenure as Utah's GM before Kevin O'Connor took over the job.
"I love the Jazz and they're a world-class organization," said Layden, who plans to work closely with San Antonio GM R.C. Buford.
Utah returned the praise.
"I want to personally thank Scotty for all his tireless work and assistance these past few years," Corbin said in the statement. "To work alongside him under coach Sloan and then to have the opportunity to have him on my staff has been a real pleasure. He is a great guy, a good friend, and while I am sorry to see him go, I understand his decision and am happy for him. I wish him and his family nothing but the very best in the future."
With Layden's departure, Corbin only has two assistants on his staff and training camp for the 2012-13 season is less than a month away.
"We want to support him the right way with what he's comfortable with, not only personality skill sets but numbers," Lindsey said. "I think we'll come up with some good potential solutions."
The Tribune's Steve Luhm contributed reporting.