The Premier League outfit have already signed Marseille midfielder Boubacar Kamara and been heavily linked with the addition of Burnley defender James Tarkowski.
However, according to The Times, Steven Gerrard will do all that he can to secure a reunion with Bassey, who he signed during his time at Ibrox.
Despite having failed to make a single first-team appearance for Leicester City before his departure in 2020, the 22-year-old is now regarded as one of the best defenders in Scottish football.
Bassey, who can play at centre-back or left-back, also put himself on the radar of many top European clubs with a strong performance against Eintracht Frankfurt in last week's Europa League final.
Although Rangers are in no rush to sell a player who still has two years left on his contract, there is an inevitability about Villa testing their resolve.