The north London club believe that the England marksman has become frustrated by his lack of opportunities as a central striker for the outgoing champions United.
Wenger wants to sign a top-level forward in the summer to replace Olivier Giroud as their first-choice frontman, and Welbeck is seen as a serious option.
And even after the sacking of manager David Moyes, Welbeck's future at United remains uncertain.
Sources close to the hitman believe he may struggle to get regular football in his preferred position, whoever replaces Moyes as manager.
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