The deal would also see Bartlett retain a significant shareholding in the club, which he purchased in June 2007.
Allam has set a Friday deadline but any potential agreement may go beyond that into next week.
It is expected that head of football operations Adam Pearson would also retain a shareholding, as well as running the club on a day-to-day basis.
Bartlett is also reportedly considering a counter offer from an as-yet unnamed American investment bank.
The Tigers, who are thought to have debts of around £30m, currently sit in 19th place in the Championship, having won only three of their opening 12 games.
Source: BBC Sport
Source: BBC Sport