The Gunners have been working on a deal for the Olympiakos centre-back for the last fortnight and held talks with his representatives in the UK last Friday in an attempt to thrash out terms.
But Roma have offered more than £2m more than the £8m Arsenal were willing to pay and have also put together a five-year package to entice the Greece international to Serie A.
Roma have moved quickly as they line up a replacement for Moroccan star Mehdi Benatia, who is closing in on a £30m transfer to Bayern Munich.
Arsenal are now weighing up alternatives to Manolas as Arsene Wenger seeks a replacement for Thomas Vermaelen, who joined Barcelona a fortnight ago.
Goal understands that the Londoners have made contact with the representatives of West Ham’s Winston Reid and they are also considering Manchester City’s Matija Nastasic.
Wenger wants to push through a deal for a new centre-back to join rookie Calum Chambers in providing cover for the established pairing of Per Mertesacker and Laurent Koscielny.
Wenger is not expected to sanction a formal move for one of his targets until the outcome is known of Arsenal’s Champions League qualifier against Besiktas. The tie is goalless ahead of the second leg at the Emirates Stadium on Wednesday night.
The Gunners are expected to make a second offer for Sporting Lisbon midfielder William Carvalho if they reach the group stages after having an initial £20m bid rejected.
Wenger is also in the market for a new striker amid fears that scans on Olivier Giroud’s foot could rule him out for a minimum of eight weeks.