Ayoze Perez or Kelechi Iheanacho are set to fill in for the injured Jamie Vardy when Leicester visit Brentford in the FA Cup fourth round on Sunday.
The Foxes will also be without defender Wes Morgan and midfielder Dennis Praet.
Championship side Brentford will be without top scorer Ivan Toney, who is suspended.
Leicester boss Rodgers insisted his team would cope without Vardy.
"We always try to rely on the collective, the group has always been able to find results," said Rodgers.
"When you don't have one of the best striker's in the league around, it's disappointing.