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United captured Bruno Fernandes in a £68m deal on Thursday, bringing an end to a long-running saga around the Portugal star.
But it is well known that they still needed a striker, with Monaco striker Islam Slimani and former Watford forward Odion Ighalo both linked with a move to United.
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However, it is 28-year-old King who has emerged as a surprise option with one day remaining in the transfer window. Bournemouth boss Eddie Howe has confirmed that United are in for the striker but hopes to retain his services.
I’m not going to deny anything that you’ve read, but I don’t want to talk too much about it. Josh is much valued and loved by us. Let’s wait and see. He’s a massive, massive part of our team. I'd be very reluctant to lose a player of that quality.
According to David Ornstein at The Athletic, United’s chances of signing King will hinge on whether Eddie Howe can sign a replacement, with Hull striker Jarrod Bowen an option but he is likely heading to West Ham instead.
The Norway international will be well known to Ole Gunnar Solskjaer, starting his career at United and making two appearances for the club before a free transfer to Blackburn in January 2013.
Since joining Bournemouth in May 2015, again on a free transfer, King has scored 45 goals in 151 league appearances. However, he has not played since the end of December.
Solskjaer did not sound hopeful of completing the deal when asked on Friday.
“I'm not sure, I don’t expect any more business to be done,” said Solskajer. "I don’t think anything is going to happen.
“Sometimes I say something here and something else happens, sometimes I say I'm happy with a player and he gets a different message, so I don't want to help or make speculations grow more and more today."