Deila has come under pressure this season due to Celtic’s disappointing results in Scotland and in Europe.
The Bhoys are just four points clear at the top of the Scottish Premiership table at the moment.
Celtic are also out of Europe, and Deila’s credentials of guiding the Hoops to success in the long run have come under scrutiny.
Rangers boss Warburton has said that he feels sympathy for the Norwegian manager.
"I referred to the goldfish bowl and it is a really passionate football city,” the Englishman told talkSPORT. “I thought London was a football city and then you come to Glasgow and really they live and die for their football.
"There's 14-15 pages every day in the papers, there are radio shows every evening, and it's scrutiny beyond belief. The fans phone in and it fuels the fire.
"So, he's top of the league. They had a difficult European campaign, okay, but what more can he do? I do feel some sympathy for him but I think you know when you join a club like Celtic or Rangers, you know what you are putting yourself up for, that's for sure."
Rangers are at the top of the Scottish Championship table at the moment with 69 points from 27 matches. The Glasgow giants are 12 points clear of second-placed Falkirk and have a game in hand.
The Gers are now virtually certain to win the Scottish Championship title and gain automatic promotion to the Scottish Premiership at the end of the season.
Rangers and Celtic will face each other in the semi-finals of the Scottish Cup this season.