The Daily Express claims that the former Arsenal striker will be allowed to leave Barcelona after just one disappointing season at the Nou Camp.
And the paper claims that his favoured destination would be Stamford Bridge, home of the Gunners' bitter capital rivals.
But he has so far failed to find top form in Catalonia as Frank Rijkaard's side have endured a frustrating season.
The Express says Barca are willing to let him leave at the right price, and also claims that the player's representatives have made initial contact with the Blues.
And if Didier Drogba - a target for both Inter Milan and Real Madrid - does leave in the summer he could be the ideal replacement.
Henry still has three years remaining on his Nou Camp contract.