The Serie A side are desperate to land the former Sampdoria man, but are facing competition from a number of clubs, including Spanish heavyweights Atletico Madrid.
Arsenal are ready to let Torreira depart the Emirates Stadium if the offer on the table is acceptable.
And Torino are trying to convince Arsenal to accept their proposal.
At present the Serie A club have board members in London to hold discussions with Arsenal for Torreira, according to Italian broadcaster Sportitalia.
All eyes will be on whether the club can present an offer which Arsenal decide to accept.
Torreira’s stock in Serie A remains high due to a successful spell at Sampdoria which convinced Arsenal to splash the cash to take him to the Emirates Stadium.
He has struggled to make his mark though and could be a casualty of Mikel Arteta’s transfer window shake-up.
