The Daily Mail says former Chelsea manager Frank Lampard would be interviewed by the Canaries about the head coach's job and that meeting is understood to have now taken place. Further discussions with the former Chelsea head coach are set to take place on Friday.
Lampard has been one of the club's preferred options since Daniel Farke was sacked last weekend but Smith - who was sacked by Aston Villa over the weekend - has also now emerged as a serious contender.
Indeed, Norwich have also discussed the vacancy with Smith over the past few days and is understood to have impressed in his discussions.
Smith was not initially available when Norwich parted company with Farke on Saturday evening; an indication that Lampard was the club's leading option at the outset of the process.
But the opportunity to speak to Smith following his sacking at Villa Park was too good an opportunity to turn down.
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