Torreira is not in Mikel Arteta’s plans at the Emirates Stadium and is expected to move on from Arsenal again this summer.
The Uruguay international spent last term on loan in Serie A at Fiorentina and his stock in the Italian top flight remains high.
Sampdoria have now kicked off talks with Arsenal aimed at signing Torreira, according to Italian outlet Il Secolo XIX.
Bringing back a player they sold to Arsenal in the summer of 2018 would be a coup for Sampdoria, who are working to a tight budget this summer.
Torreira has spent the last two campaigns away from Arsenal on loan, with a stint in Spain at Atletico Madrid prior to joining Fiorentina.
He featured regularly in Serie A last term, playing in 31 top flight games for Fiorentina and being booked eight times.
Torreira was sent off once, being given his marching orders in a 3-0 loss at home against Maurizio Sarri’s Lazio.