Palace boss Sam Allardyce confirmed earlier this week the club have come to an agreement with the Gunners to take 24-year-old Jenkinson on loan until the end of the season.
"I think that's negotiation between the chairman and the agent, but we appear to have an agreement with Arsenal [for Jenkinson]," Allardyce said.
Hector Bellerin has returned to first-team training following an ankle injury that ruled him out of the club's last two games, but Wenger insists the Spaniard's absence has not played a role in the Jenkinson deal dragging out.
"It [Jenkinson's loan] is not necessarily linked to that, but Jenkinson is a possibility to go to Palace but it is not finalised," Wenger told a press conference on Thursday ahead of the Premier League clash with Burnley. "It is basically down to him to finding an agreement with them."
Jenkinson and Mathieu Debuchy would have both hoped to be squad options for Wenger this season as Bellerin's understudy.
But Wenger is satisfied to let both right-backs leave in January having been impressed with Gabriel's performances when shifted out to full-back.
When asked if Jenkinson's move affects Debuchy's exit, the Gunners boss replied: "It doesn't affect him. Recently I've played Gabriel there and I am happy with him in that position."
Outgoing deals are likely to be the only transfer business at the Emirates during the January transfer window with Wenger once again playing down the possibility of any additions, stressing the return of Danny Welbeck has addressed any concerns over lack of depth in attack.
"I expect it to be very quiet period because we have Welbeck coming back offensively, we are very strong, and we have many players who can come. Overall I don't expect to do anything special."