"Cole needs to train but we hope he will be ready for the Stoke game on 25 April," said boss Carlo Ancelotti.
"He (Cole) is doing very well. Essien will be one week later than Cole, but he is also doing very well."
Chelsea's defensive options have been stretched of late with Cole, Branislav Ivanovic and Jose Bosingwa all ruled out.
How much have Chelsea missed Cole and Essien? However, Ivanovic, who has been out since injuring his knee against Blackburn on 21 March, trained on Thursday and could feature on the substitutes' bench for the FA Cup semi-final against Aston Villa on Saturday.
Should Cole, 29, return on the expected date, the left-back will be able to play in Premier League games against Stoke, Liverpool and Wigan and the FA Cup final, should the Blues overcome Villa.
It will also provide him some vital first-team action before Capello announces his initial 35-man squad for the World Cup on 12 May.
"Ashley is an important player for England and after the season they still have a month to get ready, so he will be ready for sure, but I have not spoken to Capello," said Ancelotti.
England kick off their World Cup campaign against the United States in Rustenburg on Saturday 12 June.
Midfielder Essien, who will also be at the World Cup with Ghana, has been out of action since January following an injury to his left knee.