The 19-year-old French defender is yet to make a senior appearance under Mikel Arteta this season after returning to north London from a loan spell at boyhood club Saint-Etienne.
The Athletic says Saliba's preference is to stay in the UK if he is to leave the club next month.
It is hoped staying put in the UK will speed up his adaption to British football but there are also options for him to return to France.
Saliba was signed by Unai Emery and then loaned straight back to Saint-Etienne, returning to find the Spaniard gone and Arteta in charge.
He is said to have made 'massive improvements' during training but the hectic schedule of this season has made it hard for him to make an impact during sessions.