The Toffees are still in the market for further signings but are also looking at the possibility of facilitating exits for several of their fringe players.
Everton boss Frank Lampard wants to revamp his midfield and the club are open to selling midfielders Andre Gomes and Allan.
The Brazilian arrived at Goodison Park from Serie A giants Napoli in the summer of 2020 and could be handed an opportunity to return to Italy in the ongoing window.
Serie A giants Roma are on the hunt for new midfielders and Allan is one of the players on their transfer wish list.
And according to Italian daily Il Messaggero, Roma could snap up Allan in a low-cost deal as his asking price is below the €10m mark, less than half the Merseyside giants paid to sign him.
Allan is in the final year of his contract at Everton and is not on the best of terms with the club at present.
It remains to be seen whether the Brazil international will move to the Italian capital this summer, while Everton are currently in talks with Manchester United over a deal for their midfielder James Garner.