Manchester United launching an improved late bid for Joshua King is dependent on Bournemouth signing a replacement striker before the transfer window closes.
Bournemouth rejected a £20m bid for the Norway international, who has 18 months left on his contract, after he emerged as a late transfer target for United to cover for the injured Marcus Rashford.
Should Bournemouth bring in another striker, United may return with a second bid before Friday's 11pm deadline.
Solskjaer indicated the club were unlikely to to make another signing, following the arrival of midfielder Bruno Fernandes on Thursday, ahead of Saturday's home Premier League match against Wolves, live on Sky Sports.
"I don't expect any more business to be done, but sometimes I say something here and then something else happens," Solskjaer said.
"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. I expect nothing to happen, but that doesn't mean that it can't happen."
Speaking also earlier on Friday, Bournemouth manager Eddie Howe said the club wanted to keep King but did not rule out his departure.
Earlier this month, former Watford striker Odion Ighalo and Leicester's Islam Slimani emerged as two of a number of players United were considering.
However, Ighalo's representatives have told Sky Sports News United have made no approach about a move to Old Trafford.
The Shanghai Shenhua striker has two years left on his contract and is currently in pre-season training in China.
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