The 48-year-old, who was dismissed by Southampton in January after a three-year stint at St Mary's, is expected to take over ahead of Saturday's Premier League match at Arsenal and the club have called a press conference for 9.15am on Tuesday.
The Royals sacked Brian McDermott two weeks ago - just 33 days after he was named manager of the month - with Academy director Eamonn Dolan taking charge.
With just eight league games remaining Reading face a desperate fight against relegation - in 19th place and seven points adrift of safety.
Former Swindon boss Paolo Di Canio had been linked to the post, as well as Roberto Di Matteo, while Brighton's Gus Poyet is said to have turned down the Madejski Stadium job.
Adkins has also been linked with Leeds United and Leicester City in recent weeks.