The defender trained at Valencia's Paterna complex on Thursday alongside a rehabilitation coach, taking advantage of his long-standing connection with the club where he developed.
Mundo Deportivo reported that Mosquera worked individually at Valencia's Ciudad Deportiva while continuing his recovery from the hamstring problem that has kept him out since the end of August.
Mosquera has remained close to Valencia since leaving for Arsenal, not least because his brother Yulian is still part of the Spanish club's academy. He regularly returns to Paterna during breaks and was able to use the facilities again while recovering.
His latest visit came after he attended Arsenal's 3-0 defeat at Brighton despite being unavailable to play. Mosquera has not featured since being forced off during the 1-0 victory at Aston Villa on August 31.
The 21-year-old had started Arsenal's opening two Premier League matches after joining from Valencia, but his injury has since left Mikel Arteta without one of his preferred options at centre-back.
William Saliba has also been absent, leaving Gabriel Magalhães alongside Ezri Konsa in the heart of the defence.
Mosquera's return to training at Paterna is an important step, although his precise timetable for an Arsenal comeback remains dependent on his recovery.
The Spaniard's relationship with Valencia has made the current rehabilitation process particularly straightforward. His brother remains at the club and Mosquera has continued to maintain links with the academy and staff who helped develop him.
Mosquera came through Valencia's academy after joining in 2016 and made his first-team debut in January 2022. He went on to make 90 competitive appearances for the club before moving to Arsenal in 2025.
His return to Paterna also comes at a difficult moment for Valencia, who are struggling near the bottom of La Liga. Mosquera said he remains confident that his former team-mates can improve their situation after speaking to people at the club during his visit.
For Arsenal, however, the immediate concern is getting the defender back to full fitness. The club have a demanding run of fixtures ahead and will want Mosquera available again rather than risk rushing him into action.
There is hope that he can return to the matchday squad after the international break, when Arsenal host Leeds United on October 10.