Their opening bid of €15m was rejected. They have made a renewed bid of €18m that remains below the Gunners' €20m price tag.
It is now reported that the Swiss is desperate to make the switch to the Giallorossi, and he will hold talks with the Gunners.
He could reportedly hand in a transfer request such that he can give up on loyalty bonuses ahead of his potential transfer.
The Gunners have already agreed to sign Anderlecht midfielder Albert Sambi Lokonga for a fee of around €20m.
They are lining up a move for another midfielder. Xhaka appears likely to head for the exit door sooner rather than later.
He has two years left on his contract. Juventus have also been linked with him, but Xhaka has a clear preference to join Roma.
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