The Gunners, who host United in the FA Cup on Friday, were reported to have enquired about taking the centre-back on loan with the intention of signing him on a permanent deal, but were knocked back by the Red Devils.
Bailly has featured in eight Premier League games this season, but only one of those appearances has come under Solskjaer.
The 24-year-old's contract expires in June 2020, though there is an option to extend it for another two years, and talk of a move away from Old Trafford comes as no shock to Solskjaer.
“I’m not surprised if [Arsenal] do [want him] to put it that way but that’s just one of those things there’s always speculation," Solskjaer told reporters. "It’s not a big surprise.”
The former Villarreal defender is not the only one whose future remains uncertain.
United are looking to talk goalkeeper David de Gea and attacker Anthony Martial into penning new deals, and the coach is confident they can tie them down.
"I think the club’s making progress, but I leave that to the right people to do that," he added. "I don’t know really how far we are away from it but hopefully we’re going to have some good news in the coming weeks."
United have won all seven games since Solskjaer replaced Jose Mourinho on an interim basis until the end of the season, after which the Norwegian still expects to return to his former side Molde.
"Obviously the plan is to go back there but it’s one of those things," he said. "I watched parts of the game against CSKA Moscow and they lost 2-1, but my job is to improve here and help the players, so that’s not very difficult. You can spend 10 or 15 mins talking to them back home."