Real Madrid boss Jose Mourinho is said to be keen to capture Cole and the Blues are bracing themselves for a bid.
They do not want him to leave but fear he may demand a move to escape his private-life turmoil.
He suffered flak over his split from Cheryl Cole and England's flop at the World Cup will not have helped matters.
Chelsea have looked for a replacement and are keen on Benfica ace Coentrao, 22, who won rave reviews in South Africa for his attacking bursts down the left flank.