Abraham looks likely to leave Roma before the transfer deadline following the arrival of Artem Dovbyk in the Italian capital this summer.
The former Chelsea forward has been linked with a potential return to the Premier League, with West Ham and Aston Villa among the sides credited with interest.
However, rumours of interest from West Ham have been described as ‘wide of the mark’ by Fabrizio Romano, with the Irons having signed Niclas Fullkrug from Borussia Dortmund earlier in the transfer window.
AC Milan are leading the chase to sign Abraham as the Rossoneri look for a complement to Alvaro Morata and Luka Jovic at the San Siro. Abraham is understood to have agreed personals terms with Milan ahead of a transfer, with the two teams in negotiations to discuss a fee.
The 26-year-old is targeting regular football after an injury-hit 2023/24, in which the England international scored just once in 12 appearances across all competitions.
Should he move to Milan, Abraham will link up with ex-Chelsea teammates Ruben Loftus-Cheek, Fikayo Tomori and Christian Pulisic.