I've read the theory that the Huns may have been descended from the Xiongnu peoples of Ancient China and Central and Inner Asia. Historically, the Xiongnu are often considered to be a major ancestor or cousins of the Mongols.
To that end, did the Mongols have any knowledge of the Huns and Attila? Who they were and their campaigns in Europe? And did the Mongols have any theories on the origins of the Huns? Did they see the Huns ancestral kin and did they have any opinions on the Huns and Attila and how they fit into the Mongols' own narrative of destiny and conquest?
Tl;dr: I'd say it is simply extremely unlikely.
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As for the afterlife/ reputation of Attila:
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On the other hand, as for the Mongols:
References:
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(Edited): fixes typos.