Villa had a scout at Huddersfield Town's John Smith's Stadium on Saturday to see a goalless draw between the Tykes and Championship leaders Cardiff in which Connolly, 25, impressed.
The former Arsenal and QPR centre-back has been a key component of Malky Mackay's promotion favourites this season as Cardiff boast the second best defensive record in the division.
Connolly, who had a loan spell at Colchester United in 2008 - a few months before Villa boss Paul Lambert took the managerial role at the Essex club - has started 25 games for Cardiff this term.
He has earned a reputation for being a leader and a good organiser at the back as Cardiff have posted three clean sheets in their last four Championship matches. He has also scored four goals - all from set pieces.
Lambert knows he must solve his side's defensive shortcomings, particularly at defending set-pieces and may be looking at Connolly as a potential signing should Villa go down in May.