The Blues are expected to be busy in this summer transfer window as manager Ronald Koeman looks to spend the funds given to him by Farhad Moshiri.
A new number one goalkeeper is likely to be top of the list, with Tim Howard having departed the club at the end of last season.
They have Joel Robles and have signed Maarten Stekelenburg from Fulham but neither is viewed as the long-term solution in the position.
A move for the Danish goalkeeper is seen as an ambitious one, but according to the Liverpool Echo the player is thought to be open to heading to Merseyside.
They believe that he is tempted by the ambition of shareholder Farhad Moshiri, as well as the appeal of working under Ronald Koeman.
The Blues could also offer him a significant increase on his current wages of £35,000-per-week, which could also be a deciding factor should they make a serious offer for him.