Lampard had held talks with the Canaries about replacing Daniel Farke, but is no longer a candidate. Sources close to the managerial situation at Carrow Road say he no longer wants to be considered.
The development could now see Smith, who was only sacked by Aston Villa last week, emerge as the top target for Norwich.
Norwich are currently 20th in the Premier League table, level on points with Newcastle on a tally of five but sit in last place due to their goal difference.
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