The offer, thought to have been in the region of £30million, was rejected by the Gunners, who have again insisted the 20-year-old is not for sale.
But Villa are reluctant to abandon the chase as they continue with an ambitious summer transfer strategy, aimed at bolstering Dean Smith’s attacking options.
Playmaker Emi Buendia has already been signed from Norwich for a club-record fee which could eventually rise to £38m, while Burnley winger Dwight McNeil has also been tracked.
Securing the signing of Smith Rowe would, however, deliver the biggest statement yet.
The England youth international was among Arsenal’s brightest performers last season and has been in talks over a new contract at the Emirates Stadium.
Yet while an agreement is still to be reached, Villa will believe they still have a chance of prising him away. An opening bid of around £25m for Smith Rowe was rejected by the Gunners earlier in the month.
The pursuit of Smith Rowe is not an attempt to bring in a replacement for Jack Grealish, though the Villa skipper’s future is under scrutiny amid serious interest from Manchester City.
Ideally, Villa want Grealish, Smith Rowe and Buendia to be playing in the same team next season. Talks over a new contract for Grealish, who the club value at £100m, started earlier this month.