The Norwegian spent two years in Glasgow, before being replaced by Brendan Rodgers this summer.
According to the report, the Oslo side are looking to move current manager Kjetil Rekdal into a sporting director position, with Deila set to take charge.
Valerenga are one of the larger clubs in Norway, but have had a poor season so far, and are currently in the relegation zone, one place off bottom. With half the season remaining there is plenty of time left to improve things.
Deila is set to reunite with Erik Espeseth in Oslo, having worked with him in a successful spell at Stromsgodset. Espeseth is stepping down as Managing Director at the Drammen outfit, and both he and Deila will be looking to change the fortunes of Valerenga as soon as possible.
Deila moved to Celtic Park in 2014 after Neil Lennon's departure, and had a mixed period in Glasgow despite his success in the Premiership. The Norwegian won the Tippeligaen the year before he headed to the UK, a super achievement for a club not traditionally among the biggest in the country and Deila would go on to win consecutive Premiership titles in Scotland too, with Rangers absent from the top flight.
However, the 40-year-old failed to take the Bhoys into the lucrative Champions League group stages during his time at the club, an absence keenly felt after Lennon's achievements in his final two seasons.
With former Liverpool boss Brendan Rodgers taking over at Celtic after Deila's rolling contract expired at the end of the previous campaign, it looks like the Norwegian is returning to his home country to get back into management.
Then Celtic manager Ronny Deila gestures to their fans after the game