Cullen has impressed in temporary spells at Bradford City and Bolton Wanderers over the past three campaigns, and is also said to have caught the eye of new boss Manuel Pellegrini in West Ham training.
And it is claimed the Chilean plans to involve the midfielder in his plans for the coming campaign, to the disappointment of Blackburn, Preston and others.
West Ham recently added Jack Wilshere to their options in Cullen's position, although speculation continues to surround the futures of Pedro Obiang and Cheikhou Kouyate at the London Stadium.
And having also strengthened in the 22-year-old's position, neither Blackburn (Joe Rothwell and Jacob Davenport) nor Preston (Ryan Ledson) should be too concerned by West Ham's stance.
Are West Ham right to deny Cullen a move to Blackburn or Preston?