The 19-year-old Real Betis star is one of several players under consideration with boss Unai Emery keen to strengthen in wide areas ahead of next season.
But a deal is unlikely to be cheap, with reports in Sevilla saying Villa have been told any agreement must be worth at least £25m.
The possibility of including a player in the deal has not been ruled out, with Betis believed to be interested in Alex Moreno. Midfielder Enzo Barrenechea has also been touted as a potential makeweight.
Moreno spent last season on loan at Nottingham Forest after falling behind Lucas Digne and Ian Maatsen in the pecking order.
Barrenechea, who joined Villa from Juventus a year ago at the same time Douglas Luiz moved in the opposite direction, impressed during a season-long loan spell in Spain with Valencia but it is not clear whether Emery views him as part of the first-team plans next season.
Villa are in the market for a winger with Leon Bailey the subject of serious interest from clubs in Saudi Arabia.
Rodriguez enjoyed a breakthrough season in Spain, making 32 senior appearances after making his first-team debut last October.
That included a second half substitute appearance in last month’s Conference League final defeat to Chelsea.