Reports in Germany claim the Bavarian giants have reached an agreement on personal terms with the 25-year-old forward and are now in discussions with Chelsea over the structure of any deal.
The London club have been telling suitors they want as much as £80million for Jackson.
Such an amount is well beyond the means of Villa, who are also struggling to pay the loan fee currently being demanded.
Unai Emery is keen to be reunited with Jackson, whom he previously managed at Villarreal, in order to inject some fresh energy into his team’s attack.
But the financial restrictions under which Villa have been operating all summer have made things tricky.
A possible loan deal for Jackson’s team-mate, Christopher Nkunku, has also been discussed. In addition to a forward, Emery would also like to recruit a right-sided defender before next week’s deadline.
Villa, meanwhile, will be without Boubacar Kamara for Sunday’s visit of Crystal Palace after the midfielder was ruled out for several weeks with a hamstring injury.
Kamara was forced off early in last weekend’s 1-0 defeat at Brentford and though initial scans have indicated the issue is not too serious, the 25-year-old is expected to be sidelined for up to three weeks.
That will definitely rule him out of the clash with Palace, with Villa hopeful he may be able to return for the trip to Everton immediately following the international break.