The FTSE 100 cigarette company announced a $56.50-per-share bid for the 58 per cent of Reynolds American it does not already own in October. This bid valued Reynolds at around $47bn.
Taking full control of Reynolds would open a valuable door in the US market for BAT.
Some 43 per cent of the offer, or $24.13 per share, was in cash, with the remainder in BAT shares.
Negotiations have centred on altering the cash-share balance, the Sunday Times reported, and BAT has indicated it is willing to add more cash to the deal.
It was reported that this alteration could add a small amount to the overall price as well as reducing the stock offer.
BAT’s share price has tumbled six per cent to £45.09 since it announced the takeover approach, while Reynolds’ is up 20 per cent to $55.54.
It was reported that BAT could offer an additional $8 per share to the offer and could be announced as soon as this week.
BAT declined to comment.