The Hammers had a £2 million bid rejected by Rovers for the Sweden international and the incoming boss says that, until an offer comes in which they feel represents the true value of their player, he will remain at Ewood Park.
"Nothing is happening at the minute," Appleton told reporters at his unveiling to the press at Blackburn on Thursday. "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.
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"We have a couple of weeks left [of the transfer window]. 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."