Hammers manager Sam Allardyce lodged a £2million bid for the Swede, which was turned down flat.
Although Allardyce had insisted he was not prepared to increase the bid, it is thought a further offer may be on its way.
However, Olsson remains a Rovers player for now, with Appleton insisting the 24-year-old will not be allowed to leave on the cheap.
"Nothing is happening at the minute," said Appleton.
"I was made aware of a bid that was put in before I took the reins but it is way below the value we see him at.
"Until a bid reaches the valuation we think it should be, there is not a conversation.
"Martin continues to be a Blackburn player.
"He is a fantastic player, an international with bags of talent, and I am looking forward to working with him."
However, with Olsson hoping to leave Ewood Park this month, a transfer does seem likely eventually.
Indeed, Appleton believes a certain amount of movement would actually be healthy for a club that desperately needs to kick-start their season if they are to stand any chance of reclaiming their top-flight status.
"We have a couple of weeks left," he said.
"As with any football club, some players will leave, others will come in. But a few new faces will do the club a world of good.
"It will bring fresh competition, but it has to be players who will affect the starting XI, not the 18."