The Hoops legend says defeat to Rangers is "unimaginable".
The Norwegian is under fierce pressure with the Hoops as his side continue to make hard work of winning the Scottish Premiership amid the threat of Aberdeen, who sit just one point behind them with nine games to go - eight for the Dons.
Celtic's failure to make much of an impact in Europe has done Deila no favours after the Bhoys were eliminated from Champions League qualifying in each of the last two years, before finishing bottom of their Europa League group this season.
The reigning Premiership champions were paired with their bitter rivals in next month's semi-final at Hampden Park, and Thompson feels that there is no way back for the 40-year-old if he loses the Old Firm derby.
“The manager is under enough pressure as it is because of the league situation," he told The Scottish Sun.
“If he’s still there and doesn’t win that game then that would have to be the straw that breaks the camel’s back. It would be unimaginable for Celtic to lose."
The Rangers clash takes place on April 17. They face Kilmarnock in the league next Saturday, before welcoming Hearts to Parkhead the following week.