Norwich sacked Farke on 6 November, only hours after the German had overseen the Canaries’ first win of the Premier League season in a 2-1 victory at Brentford.
Smith is expected to make his decision over the weekend but is understood to be keen on a quick return to coaching.
Farke’s spell as Norwich boss was ultimately ended by his side’s chastening 7-0 defeat at Chelsea on 23 October, even though he remained in the job a further two matches.
Smith lost his job at Villa after five straight Premier League defeats, with the Birmingham club’s last victory coming on September 25 with a 1-0 win at Manchester United.
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