David Alaba has made a decision over his future amid Manchester United’s willingness to sign the defender on a £12million-a-year deal.
And Daily Star exclusively reported last month that United had also put their hand in, speaking to Alaba’s representatives.
But Spanish outlet Marca have reported that United are set for disappointment.
Alaba is now “very close” to signing for the Bernabeu side, with the club wanting to make an announcement next week.
Bayern chief Karl-Heinz Rummenigge has accepted defeat in Bayern's attempts to keep Alaba and he said: "We had a lot of conversations, but we wanted answers from him by the end of October.
“This didn't happen and I don't know if we'll return to the negotiations. What I want to be clear about is that our offer showed exactly how much we value him, but he didn't accept it."
Alaba has been with the Bundesliga giants since 2009, graduating from the academy to make more than 400 appearances.
And the Austrian has helped his side win nine league titles as well as two Champions League honours.
Solskjaer is still keen to strengthen his defence to ease the growing burden on Harry Maguire and Victor Lindelof.
While they are set to welcome teenager Amad Diallo to Old Trafford this month, having signed him from Atalanta in October.