Smith has also been linked with a move to Crystal Palace, whose manager Patrick Vieira is said to be an admirer of him.
Aston Villa are increasingly monitoring the Scottish market following the success of midfielder John McGinn in the Midlands, while Gerrard is aware of Smith’s potential having worked north of the border as Rangers boss.
Scotland Under-19 internationalist Smith made his Dundee United debut last year, a day after turning 16, and played against Rangers when Gerrard was in charge back in February.
Aston Villa are also looking at signing Scottish full-back Aaron Hickey, who is currently performing well for Bologna. A fee of £20million has been mooted for the ex-Hearts youngster.