The Gunners are reported to have joined Liverpool in the race to sign Downing, who made it clear when on England duty last month that he will not be signing a new contract with Villa.
But sources close to the Midlands club insist any possible interest has not been firmed up so far and new manager Alex McLeish wants to keep the former Middlesbrough player.
Villa have already rejected bids of £12million and £15million from Liverpool for Downing, who has two years remaining of his current contract.
If Villa find they are eventually left with no option but to sell Downing, then they will hold out for their original valuation of £19million.
Wigan's Charles N'Zogbia has been linked with Villa as a possible replacement should Downing leave.
McLeish came close to signing N'Zogbia last summer when in charge of Birmingham before a change in his wage demands ended hopes of the deal being completed.
Villa are also monitoring West Ham midfielder Scott Parker, although no bid has been made.
But the club finally expect the signing of Manchester City goalkeeper Shay Given to go through at some stage this week in a £3.5million deal.