The Arsenal loanee has managed to shake off a knock he picked up in the summer, which saw him sidelined for nearly two months.
Jenkinson is quoted as saying by Sky Sports News: "The coaching staff and physios are being careful with me as I was out for six weeks and before the Hull game I only trained for two days.
"I was out for quite a long time, you can't just throw someone back in.
"I don't know whether I will start from now on but my fitness feels good and I will keep working hard but it is the gaffer's decision. I think I am ready to start."
Jenkinson came off the bench in West Ham's last two games, against Hull City and Liverpool.