Palmer, tied with Manchester City's Erling Haaland as the Premier League's joint top scorer with 20 goals, missed Tuesday's thrashing at Arsenal through illness.
He has recovered, however, and will be part of the squad as Chelsea seek to close a six-point gap with sixth-placed Manchester United.
"Yes, Cole was training well in the last few days. We assume he is going to be ready for tomorrow, be part of the squad," Pochettino told reporters on Friday, ahead of visiting fourth-placed Villa.
"Cole is a very good player... a key player for us and he is showing we struggle a little bit without him."
Chelsea were hit with an injury blow on Thursday when midfielder Enzo Fernandez was ruled out of their remaining games this season after undergoing groin surgery.
Chelsea, ninth with 47 points from 32 matches, face Villa on after consecutive losses, including a 1-0 defeat to Manchester City in the FA Cup semi-finals.
"It's testing everyone in the club," Pochettino said. "We are not in the place we wanted to be.
"We need to be positive. It's the only way to move forward. Never give up.
"We're going to push and get the best from the players we have in our hands.
"We cannot give them the excuse to not perform and not to be focused but at the same time, we are people, we are not machines."
