The 19-year-old has been heavily linked with a move to the top flight after impressing last season for the Blues, as well as putting in a number of solid displays for the England Under-21s.
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He told the Birmingham Mail: "The truth, me being transparent and not speaking out of line, is that there are six to eight Premier League clubs interested in Nathan. That's in various different ways.
"Sometimes you get a call from an agent, then get a call from the player's agent, sometimes you get an enquiry from a fellow manager.
"Now what we have had are three bids, two that have been accepted and one that hasn't been accepted. And now it's up to Nathan if he wants to speak to those two clubs and see if it's right for him."
Clark also warned other interested clubs they will have to make an offer which meets Birmingham’s valuation to stay in the running for the wideman.
"What those other clubs have to do who haven't put bids in yet is get to the level where the other two are at,” he added.
"It's another one where you don't want to lose the player, but you understand the reasons why he has to go. Unfortunately that's where we are at the moment and we have just got to get on with it."