The Baggies are battling interest from fellow Championship clubs, including Queens Park Rangers, for the 25-year-old's services.
Onomah, a former Tottenham youth product, has previously had a loan spell with Steve Bruce at Villa before joining Fulham on a permanent deal in 2019.
Should Albion win the race for the box-to-box midfielder it will be a third spell working together as Onomah also played under Bruce on loan at Sheffield Wednesday.
He has made 54 appearances in all competitions for the Whites, including 11 in the Premier League.
Bruce is keen to bolster his midfield having allowed Alex Mowatt to leave on loan for Middlesbrough. Albion were beaten to the loan signing of Manchester United's Hannibal Mejbri by Blues.
Albion are keen on another forward, a midfielder and a defensive recruit on deadline day, which ends at 11pm.