Arsenal have suffered multiple injuries recently, with Mathieu Debuchy now ruled out for up to three months.
Gold, however, has taken to Twitter to confirm that Arsenal cannot end the right-back's loan spell at Upton Park.
“@Ray63Stokes: can Arsenal take Jenkinson back this month, after injury to Debuchy No, he's contracted to us till the end of the season. dg— David Gold (@davidgold) January 15, 2015
Jenkinson has impressed down the right-hand side for West Ham so far this season and Sam Allardyce will no doubt welcome the official clarification of the Hammer's transfer status.
The striker struggled in east London after being accused of being overweight and failing to adapt to the physical demands of the Premier League.