Tuchel has been linked with Ruben Amorim's job as the Portuguese continues to struggle in the hotseat.
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Former Chelsea and Bayern Munich coach Tuchel held talks with United after Erik ten Hag's axing, but was left unimpressed by the actions of their management team.
The Sun says should Amorim be dumped in the coming weeks, the German will not consider applying for the job.
Sources say he was "distinctly unimpressed by United’s process" before ultimately taking on the England job.