The 28 year-old, who turned down a fight on June 13 with compatriot Kell Brook, is hoping to face the New Yorker on his home turf at the Barclays Center.
Algieri, 31, went the distance with Manny Pacquiao in his last fight, the only reverse on his record, and holds victories over Ruslan Provodnikov and Emanuel Taylor to his credit.
Khan states in the video that the remainder of the details will be announced soon by advisor Al Haymon as the former 140lb champion looks to build on his impressive wins over Devon Alexander and Luis Collazo since moving up.