"I think he needs some more days to train but we hope he will be ready for the game against Stoke (on April 25)," manager Carlo Ancelotti told reporters on Thursday.
"He is doing very well and so is Michael Essien. Maybe he will be one week later (than) Cole."
Ghana midfielder Essien has not played for the club since injuring his hamstring in December. He then suffered a knee problem at the African Nations Cup in January.
Leaders Chelsea are two points clear of Manchester United in the Premier League, with Arsenal a further point adrift and five games remaining.
The game against Stoke City comes directly before their last two league fixtures against Liverpool and Wigan Athletic.
Cole, England manager Fabio Capello's first-choice left back, has been fighting to get fit before the end of the season with the World Cup starting in South Africa on June 11.
The 29-year-old broke his left ankle at Everton at the start of February but returned to light training last month.
Ancelotti also said Serbia international Branislav Ivanovic trained on Thursday and could be on the bench for the FA Cup semi-final against Aston Villa at Wembley on Saturday.
The defender has been out since he hurt his knee at Blackburn Rovers on March 21.
