Jenkinson has not played for the Gunners since November 5 after suffering a stress fracture in his back.
The 20-year-old, who has made 11 appearances since signing from Charlton last summer, made a successful 45-minute comeback in Arsenal's reserve win over Norwich on Tuesday night and could come in to consideration for Sunday's game at the Emirates Stadium.
Reserve team coach Neil Banfield said Jenkinson's return was "nice to see". While the versatile defender would not be assured of a place in Arsene Wenger's starting XI, his availability would be welcomed given that the under-fire Gunners boss has a number of injury concerns at the back.
Per Mertesacker is out with a long-term ankle injury, Laurent Koscielny missed last weekend's defeat at Sunderland, while Sebastien Squillaci and Francis Coquelin both hobbled off at the Stadium of Light and will miss Sunday's game.
Wenger only has two other fit centre-halves - Thomas Vermaelen and Johan Djourou.