While details such as length of contract, salary and budget are yet to be agreed, it is believed that Henry has held talks with Villa's majority shareholders Nassef Sawiris and Wes Edens.
Whilst Henry is keen to take the reins at Villa, Bruce's future needs to be sorted, as do a contract for Henry and discussions about the club's transfer budget.
However, the 57-year-old is still yet to meet Sawiris and Edens.
He said he was "absolutely delighted" when asked about staying as he arrived for Villa's 3-1 friendly defeat to West Ham.
His first full season in charge nearly brought a return to the Premier League as Villa reached the Play-Off final, but his side were beaten 1-0 by Fulham at Wembley in May.
Bruce is on a rolling contract at Villa and has already missed out on promotion to the Premier League with the club twice.
Bruce has been linked with a move away from Villa following the arrival of their new owners.
"I'm mindful that both economically and the wish of the player dictates that it's hard to keep that quality of player, but what I would say is that we want to try, and if he enjoys what he's doing and if he likes what we're trying to achieve in terms of how we're playing then who knows".
Villa still need to find £40million to comply with Financial Fair Play rules, with midfielder Grealish their most saleable asset.