The former Arsenal defender, who won 12 major trophies with the Gunners, sent a job application via email to the Football Association of Singapore (FAS) according to Goal.com.
Adams told Channel NewsAsia via text message: "Got a couple of opportunities a bit closer to home but I know the FAS (Football Association of Singapore) are looking for a new coach."
His application may appeal to the FAS after his stint as sporting director of Chinese Super League side Chongqing Dandai Lifan for just over a year between 2016 and 2017.
The 51-year-old became caretaker manager of Spanish side Granada in mid-April last year, and the (admittedly doomed) Andalusian club were relegated under his tenure after seven consecutive defeats.
Following relegation, Adams stood defiant and blamed his players for the troubled spell.
"I think nothing was going to work with this group of players," the former Gunner said.
"I think we've tried every formation, just like Lucas (Alcaraz, his predecessor) did. We've had three coaches, and we've had the same results, so you have to look at the players."
Singapore are currently 172nd in the FIFA world rankings. Ex-Sunderland manager Terry Butcher and former Wolves boss Dave Jones are also reportedly interested in the job.
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