Rosenberg did not feature for the Baggies against Liverpool at the weekend.
"Markus didn't even make the squad at the weekend," West Brom manager Steve Clarke told the club's official website.
"He was probably just a week too late joining us.
"If he'd been a week earlier, Markus would have made my job even more difficult. He's coming on, he's great.
"We had a training session with the substitutes and the players who weren't involved on Sunday. Markus was electric in training, so he's looking good. He'll be in the travelling party to go to Tottenham."