The Cottagers and Newcastle United have both been chasing a deal for Bent in recent weeks, with Villa open to the sale of the England international forward.
With Newcastle reported to be unwilling to meet Villa's valuation of the striker, Fulham have lodged a second bid for Bent today, according to Sky Sports News.
An improved offer from the Cottagers is believed to be in the region of £5m, as manager Martin Jol looks to boost his attacking options this summer.
Bent joined Villa for a club-record fee of £18m two years ago, but found first-team opportunities limited under manager Paul Lambert last season.
The 29-year-old scored six times in 23 appearances during a frustrating campaign.