The England striker's deal expires at the end of this season and Moyes has confirmed talks over an extension have yet to commence.
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He explained on BBC Sport: "There's not been a contract offer since I've been here, it was under a different regime.
"We want everyone to have to fight for what they're doing and show what they're worth. We're taking a lot of time to look, unfortunately Dom has been injured for a big part of it.
"But his history has been very good so we will take all that into consideration."