The Three Lions boss reveals he will add the Gunners right back to his ranks ahead of next week's Sweden friendly if he receives permission from the sport's governing body.
The Gunners' full back has impressed in the early stages of the season, and the England manager is adamant he wants the former Charlton man in his side, but he has to wait for permission due to the player's previous appearances for Finland at the Under-21 level. Jenkinson is eligible to apply for a one-time switch under FIFA rules and has not played for Finland in an official 'A' competition, which should make him eligible for England.
Jenkinson made the commitment to play for England last month and was included in a training squad before their games against Poland and San Marino.
"The reason I didn't include Carl from the start is because we haven't, at this moment in time, got clearance from FIFA, but we do believe that they are going to grant that clearance within a day or two," Hodgson told the FA's official website. "So by next Wednesday, he will be clear to play. He wants to play for England and has made that clear so we applied for permission to FIFA, as one is allowed to do, immediately after he left us and before we set off for Poland.
"That was a month ago, but I didn't want to put his name down in a squad until such time as I've got FIFA clearance saying he's available to play for us in my hand.
"If the clearance comes through, we will put him in the squad. He was with us for training just before we left for Poland, and I made it clear to him then that if he did want to play for England, I would include him in this squad and I intend to keep that promise."