The Australia paceman signed a two-year deal at Trent Bridge last November, but he will be unable to fulfil his duties this term due to back and ankle injuries.
As a result, Notts are eager to bolster their attack by signing an overseas bowler in the near future.
"It's obviously disappointing, most importantly for Peter himself and we wish him well for his recovery," Newell told the club's official website.
"An experienced overseas bowler is a key position for us and we're confident of signing a player of sufficient quality in time for the start of the season."
Siddle, 31, is expected to return to Nottinghamshire for the 2017 campaign.