The 20-year old right-back was not included in Hodgson's initial 23-man squad for the November 14 fixture in Stockholm because he has not yet been granted permission to represent the Three Lions.
Jenkinson played for Finland at U19 and U21 level and Hodgson says FIFA need to give him permission to swap allegiances.
"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," he told FATV.
"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."