Crystal Palace are said to have agreed a £7million fee with Arsenal for Jenkinson, who has made just five senior appearances for the Gunners this term.
But despite weeks of negotiations with Palace, the right-back is yet to agree personal terms over a Selhurt Park switch.
Wenger said on the 24-year-old: "Only he has to agree personal terms but at the moment he has not managed to do that."
Palace manager Sam Allardyce recently admitted that he has not given up hope on signing the one-cap England international this month.
The 62-year-old said last Friday: "Until the chairman rings me up and says the Carl Jenkinson deal is dead, it is still ongoing for me."
Allardyce worked with Jenkinson during his time as West Ham manager when he signed the former Charlton youngster on loan in the 2014/15 season.