Denmark are seeking a permanent national team coaching appointment after Klaus Hjulmand's departure after the Euros.
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Tipsbladet says the Danes have approached Solskjaer, but the Norwegian turned down the approach.
It is said that Solskjaer declined as he is in talks about a return to manegement "with a big club".
Solskjaer has been out of football since his sacking by United in 2021.