Former Crystal Palace and Newcastle boss Pardew, 55, had been linked with replacing Alex Neil who was sacked by the Championship club on Friday.
Canaries caretaker boss Alan Irvine said after the weekend's 2-2 draw with Blackburn he expected to still be in charge against Barnsley on Saturday.
Chairman Ed Balls said Neil's sacking was the start of "big changes".
Norwich are also expected to announce some more changes this week, having been without a chief executive since Jez Moxey left last month.
Neil was sacked after just over two years at Carrow Road, following a run of five games without victory which left them nine points outside the top six.
Pardew was sacked by Palace in December, leaving them just a point above the Premier League relegation zone having led them to the FA Cup final last season.
Former Hamilton boss Neil took over at Carrow Road in January 2015, replacing Neil Adams, and led the Canaries to promotion to the Premier League via a play-off final victory over Middlesbrough.
But he was unable to save the club from an instant return to the second tier and left with them ninth in the Championship table, having previously said he believed he was the best person for the "big, big job" at the Championship club.
"Naturally, I feel very disappointed to have lost my job," the 35-year-old said. "This current season has been one of transition, with the club adjusting to the consequences of relegation from the Premier League, as well as two chief executives moving on in a short space of time.
"I have worked with some great people at the club and have shared some fantastic memories with them. I will always be very proud of our achievement of winning promotion, via the play-offs at Wembley, and of having the opportunity to manage Norwich in the Premier League.
"I would like to thank my coaching staff for their hard work and loyalty and all the players and the staff throughout the club for their efforts on and off the pitch."
Alan Pardew is not in the running to become the new Norwich City manager, BBC Radio Norfolk understands.