The 31-year-old goalkeeper has been without a club since May 2012 when he was released by Premier League side Sunderland.
Gordon has been plagued with a number of knee injuries throughout his career, and spent time training with Celtic's Glasgow rivals Rangers last season.
However, it appears the former Hearts shot-stopper is set to sign on at Celtic Park amid reports that England international Fraser Forster is set to be sold, with Atletico Madrid heavily linked with a move.
"We are getting closer with Craig Gordon, it is down to the small details. We can make this happen but it's not confirmed yet," Deila told The Daily Record.
"We need to have alternatives. You always make contingency plans.
"If you are going to bring in older players then they need to have the right mentality and Craig has that."
Gordon moved to Sunderland in August 2007 in a £9 million deal, which at the time represented a British record fee for a goalkeeper.
