The Toffees are preparing for one more year in the Premier League, with the aim of never being in a relegation scrap again.
Per The Sun, the Goodison Park club believe Abraham can fire the goals to get them higher up the table next term.
Everton are working to clinch a £27 million deal with the Italian capital club for Abraham.
Roma are struggling financially and do need the money from a sale to invest in new signings.
Manager Jose Mourinho is ready to lose Abraham, with media reports this week linking him with a loan move for Romelu Lukaku.