The newspaper claims that the 23-year-old is a wanted man in London, as the Addicks aim to get him in on another loan spell after he excelled for them this season.
The Irishman was a key part of the Charlton side who won promotion to the Championship from League One this term, claiming an assist for the winning goal in the Play Off final victory over Sunderland.
However, Cullen is expected to start pre season with the Hammers, with manager Manuel Pellegrini preparing to run the rule over him.
The Cullen situation is an interesting one for West Ham. Clearly Pellegrini was impressed by what he accomplished with Charlton this season and wants to take a look at him in pre season as a result. However, he’s 23 years of age now, he’s either going to be good enough to make the breakthrough with the Hammers or he isn’t. So this is a crucial pre season for the youngster and, selfishly, Bowyer will be hoping he fails to make the grade with the Irons. If Pellegrini decides Cullen isn’t quite up to a first team spot then he’ll probably look to offload him this summer. However, you’d have to think that if the West Ham boss isn’t impressed by him then he’d surely look to sell him at this stage rather than continue to perpetually loan him out. Whether Charlton are prepared to sign the midfielder permanently, and if they have the funds to do so, remains to be seen, though.