The Argentine wants to be the Gunners’ No.1 after an outstanding end to last season when deputising for the injured Bernd Leno.
Villa are said to have launched a second bid for the keeper worth nearer to his £20million price tag.
According to the Evening Standard, Arsenal have been offered Areola on loan as a short-term replacement for Martinez.
The 27-year-old spent last season on loan at Real Madrid, playing second fiddle to Thibaut Courtois at the Bernabeu.
Areola wants a move to the Premier League and newly-promoted Fulham are currently the favourites to sign him.
Brentford’s David Raya has also been touted as a possible replacement for Martinez, but boss Thomas Frank does not want to sell him.
Martinez has just two years remaining on his current deal and is counted as a homegrown player as he has been at the club for almost a decade.
Arsenal have already brought in Willian and Gabriel Magalhaes so far this transfer window, with Atletico Madrid’s Thomas Partey still a priority target.