Not according to the info provided by Bungie.
Xur will offer Exotic Reforging for 6 Weapons, and 6 Armor pieces. Those 6 will be available each weekend, similar to how his Exotic's sold will be.
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I thought Deej confirmed on Twitter its whatever weapons you have equipped? And its up to 3 a week ?
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Can you link me the post?
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I double checked. The only thing he confirmed was its more than 1 exotic a week...but nothing about if its random