Bowyer is said to be targeting another season-long loan deal for Cullen, who scored or made seven goals for Charlton last season.
But the Addicks boss may have to be patient in his pursuit of the 23-year-old, who is expected to begin pre-season back at West Ham as he awaits a decision on his future, according to the SLP.
Cullen is entering the final year of his contract at the London Stadium, and it's possible the Hammers would prefer a sale should they choose to part with the homegrown talent.
But there could yet be a vacancy in Manuel Pellegrini's midfield, with Edimilson Fernandes having left West Ham for Mainz this week.
Perhaps the biggest concern for Charlton will be whether or not Bowyer commits his future to the club.
The former West Ham midfielder's deal expires at the end of this month and he is said to have interest from West Bromwich Albion and Derby County.
What should West Ham do with Cullen?
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