Wales international Hennessey missed last weekend's trip to West Brom after pulling up injured during the warm-up.
That forced veteran crowd favorite Julian Speroni to don the gloves, and the 38-year-old excelled in keeping a clean sheet during the goalless draw.
Boss Roy Hodgson confirmed that Hennessey is back in training and available to face the Cherries - but gave no guarantee that he would regain his spot.
"Wayne trained for the first time [on Thursday]," said Hodgson.
"His back went into spasm during the time he was warming up. It has happened to him three times before and it was just very unfortunate that it happened on the day of a game.
"He missed the first three days of training this week but was out there training in a modified form, and will train fully on Friday.
"There is a stiff competition between the two of them always which is always something for me to resolve before a game because they are both very competent.
"Wayne Hennessey kept a clean sheet (against Brighton) before Julian, and now Julian has kept one. So they are keeping me on my toes."