Cottagers boss Martin Jol is desperate to land a striker who will take some of the pressure off last season's leading scorer Dimitar Berbatov.
Bent was reportedly the subject of a £4m bid from Fulham last month, which was rejected by Villa, but they are believed to have made an improved offer of around £5m.
Newcastle were also linked with the 29-year-old but their interested has cooled, with Alan Pardew linked with a move for QPR's Loic Remy.
Bent was a peripheral figure for Aston Villa last season, mainly due to the impact made by Christian Benteke, and they have further strengthened their attacking options this summer.
Bent cost Villa a club-record £18m - rising to £24m - when they signed him from Sunderland in 2011. He has two years remaining on his contract at Villa Park.