Old Trafford chiefs snubbed an enquiry for their Premier League rivals to take the 24-year-old on loan for the rest of the season.
Speaking at a press conference ahead of tomorrow’s FA Cup tie against the Gunners, Solskjaer said: “I’m not surprised if they do, to put it that way but that’s just one of those things there’s always speculation.
“It’s not a big surprise.”
Arsenal are eager to sign a defender after losing Rob Holding and Hector Bellerin for the rest of the season to injury.
Emirates Stadium chiefs are only looking at loan deals due to financial restrictions.
A swoop for Bailly until the end of the campaign with a view to a permanent switch in the summer was being explored.
But Manchester United flat-out refused their enquiry because they do not want to help out a rival.
The two clubs are level on points in the race for a top-four spot.
Bailly has been out of favour at Old Trafford since the start of the season.
Despite the departure of Jose Mourinho, he has still failed to battle his way back into the starting XI.
The Ivory Coast international has started one of Solskjaer’s seven games in charge.
— United Xtra (@utdxtra) January 22, 2019
Bailly has 18 months left on his contract and United have an option to extend for a further two seasons.
They are waiting until a permanent manager is identified before deciding on his future.
Solskjaer takes his side to north London tomorrow night for an FA Cup fourth-round tie.
Chris Smalling, Marcos Rojo and Marouane Fellaini are not available due to injury.
“Smalling has started training so hopefully he’ll be available maybe next week, so it’s looking good for him,” Solskjaer said. “Fellaini and Rojo are still a bit away.”