Saliba, 25, will not require surgery on the injury sustained during France's World Cup semi-final defeat to Spain but is expected to miss the start of the Premier League season, leaving Mikel Arteta with only Gabriel Magalhães and Cristhian Mosquera as recognised centre-back options.
A deal for a defender could be completed before Arsenal finalise their move for Newcastle's Bruno Guimarães, reflecting the urgency of the situation.
Beyond Fresneda and Ramón, two of his Sporting team-mates have also been mentioned: Zeno Debast, who has been offered to Arsenal via intermediaries for a fee in the region of €40m (£34m), and Gonçalo Inácio, who has long been linked with a Premier League move and is understood to be a primary target for AC Milan this summer.
Debast missed the entirety of Belgium's World Cup campaign after picking up a thigh injury in May, though manager Rudi Garcia had taken him to the tournament in the hope he would recover in time to feature in the knockout rounds; the 22-year-old made 72 appearances for Sporting last season, including 12 in the Champions League.
Ramón, 21, spent time in Real Madrid's youth system under current Chelsea boss Xabi Alonso before joining Como, and any move for him would be complicated by the 50% sell-on clause and buy-back option Real Madrid retained when he left the Bernabéu; Chelsea have also monitored his situation but are now closing in on Crystal Palace's Maxence Lacroix instead.
Arsenal have also considered Aston Villa's Ezri Konsa and free agent John Stones, though the latter is understood to be closing in on a move to Inter and Villa's valuation of Konsa is seen as too demanding for a deal to progress easily.
Whichever option Arsenal ultimately pursue, the priority is a defender capable of forming an immediate partnership alongside Gabriel at the heart of the defence while Saliba continues his recovery.