The Gunners could sanction the departure of the Uruguay international before the transfer window slams shut and Fiorentina and Torino have been leading the chase to take him back to Italy.
However, according to Italian outlet Calciomercato.it, Roma are maintaining their interest in the former Sampdoria man.
A potential swap deal involving Amadou Diawara has been floated as a possibility, but Roma could still try to sign Torreira even if Diawara is not involved in the deal.
Torreira is keen to return to Italian football, where he shone for Sampdoria.
And he is claimed to be keen to make sure that when he does he joins a club also involved in European competition.
Roma managed a finish of fifth in Serie A last season, securing Europa League football, while Fiorentina came tenth and Torino finished the campaign in 16th.
The transfer window remains open for business until 5th October.