The Sun says the Blues are keen to enact their £40million buy-back option for Ake, who has developed into a top class centre-back while playing for Bournemouth.
And Chelsea are willing to listen to offers for 23-year-old Christensen.
But though there is plenty of interest in Christensen as a player, there is a shortage of clubs willing to match or improve his current £80,000-a-week wages.
AC Milan are one of the clubs who have registered an interest as they search for a new centre-back this month.
But they would prefer a loan deal for the remainder of the season with an option to buy in the summer – and are not keen to meet Chelsea's valuation of £35m for the defender.