Pogba, 26, is expected to leave Old Trafford this close season, his agent Mino Raiola having recently said the midfielder wants an exit.
However, speaking at a news conference in Perth on Wednesday, Solskjaer said United were yet to receive bids for any of their players.
"There has been loads of talks and speculations about many of our players, both ins and outs. For me, it's business as usual," he said.
"When you're at Man United, you expect all these things to pop up in the summer and of course I've been in touch with Paul, spoken to Paul, spoken to Rom, spoken to Rashy [Marcus Rashford], Jesse [Lingard], spoken to all the players more or less over the summer as you do, you keep in touch with them.
"As far as I'm aware and up until now, we don't have any bids for any of our players... Paul, or most of our players, [have] got long contracts. We are Man United, we don't have to sell players."
Pogba, who is contracted until 2021, was reported to have had a bust-up with Lingard after an exchange between the pair on Tuesday.
Solskjaer was unhappy with those reports, accusing the media of having an "agenda" against Pogba.
"It looks like there is an agenda against Paul. He's a top, top bloke. He's a great, great professional, he's never been any problems, he's got a heart of gold," the Norwegian said.
"For example, Jesse and Paul yesterday walking around, and it's been portrayed as it's a fight between the two boys. I know you're here to sell papers and sell stories, but there's no problem between the boys at all.
"They are all professional and pre-season has been very, very good so far."
Manchester United will face A-League premiers Perth Glory in a friendly on Saturday.